Analyse non supervisée
Majda & Ruxue
3/29/2021
Chargement des library
library(tidyr) #Gérer les dataframes
library(dplyr) #Gérer les dataframes##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(lubridate) #Gérer les dates##
## Attaching package: 'lubridate'## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, unionlibrary(FactoMineR)
library(MASS)##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## selectlibrary(cluster)data <-read.csv("weatherAUS.csv")
head (data)## Date Location MinTemp MaxTemp Rainfall Evaporation Sunshine WindGustDir
## 1 2008-12-01 Albury 13.4 22.9 0.6 NA NA W
## 2 2008-12-02 Albury 7.4 25.1 0.0 NA NA WNW
## 3 2008-12-03 Albury 12.9 25.7 0.0 NA NA WSW
## 4 2008-12-04 Albury 9.2 28.0 0.0 NA NA NE
## 5 2008-12-05 Albury 17.5 32.3 1.0 NA NA W
## 6 2008-12-06 Albury 14.6 29.7 0.2 NA NA WNW
## WindGustSpeed WindDir9am WindDir3pm WindSpeed9am WindSpeed3pm Humidity9am
## 1 44 W WNW 20 24 71
## 2 44 NNW WSW 4 22 44
## 3 46 W WSW 19 26 38
## 4 24 SE E 11 9 45
## 5 41 ENE NW 7 20 82
## 6 56 W W 19 24 55
## Humidity3pm Pressure9am Pressure3pm Cloud9am Cloud3pm Temp9am Temp3pm
## 1 22 1007.7 1007.1 8 NA 16.9 21.8
## 2 25 1010.6 1007.8 NA NA 17.2 24.3
## 3 30 1007.6 1008.7 NA 2 21.0 23.2
## 4 16 1017.6 1012.8 NA NA 18.1 26.5
## 5 33 1010.8 1006.0 7 8 17.8 29.7
## 6 23 1009.2 1005.4 NA NA 20.6 28.9
## RainToday RainTomorrow
## 1 No No
## 2 No No
## 3 No No
## 4 No No
## 5 No No
## 6 No Nostr(data)## 'data.frame': 145460 obs. of 23 variables:
## $ Date : Factor w/ 3436 levels "2007-11-01","2007-11-02",..: 397 398 399 400 401 402 403 404 405 406 ...
## $ Location : Factor w/ 49 levels "Adelaide","Albany",..: 3 3 3 3 3 3 3 3 3 3 ...
## $ MinTemp : num 13.4 7.4 12.9 9.2 17.5 14.6 14.3 7.7 9.7 13.1 ...
## $ MaxTemp : num 22.9 25.1 25.7 28 32.3 29.7 25 26.7 31.9 30.1 ...
## $ Rainfall : num 0.6 0 0 0 1 0.2 0 0 0 1.4 ...
## $ Evaporation : num NA NA NA NA NA NA NA NA NA NA ...
## $ Sunshine : num NA NA NA NA NA NA NA NA NA NA ...
## $ WindGustDir : Factor w/ 16 levels "E","ENE","ESE",..: 14 15 16 5 14 15 14 14 7 14 ...
## $ WindGustSpeed: int 44 44 46 24 41 56 50 35 80 28 ...
## $ WindDir9am : Factor w/ 16 levels "E","ENE","ESE",..: 14 7 14 10 2 14 13 11 10 9 ...
## $ WindDir3pm : Factor w/ 16 levels "E","ENE","ESE",..: 15 16 16 1 8 14 14 14 8 11 ...
## $ WindSpeed9am : int 20 4 19 11 7 19 20 6 7 15 ...
## $ WindSpeed3pm : int 24 22 26 9 20 24 24 17 28 11 ...
## $ Humidity9am : int 71 44 38 45 82 55 49 48 42 58 ...
## $ Humidity3pm : int 22 25 30 16 33 23 19 19 9 27 ...
## $ Pressure9am : num 1008 1011 1008 1018 1011 ...
## $ Pressure3pm : num 1007 1008 1009 1013 1006 ...
## $ Cloud9am : int 8 NA NA NA 7 NA 1 NA NA NA ...
## $ Cloud3pm : int NA NA 2 NA 8 NA NA NA NA NA ...
## $ Temp9am : num 16.9 17.2 21 18.1 17.8 20.6 18.1 16.3 18.3 20.1 ...
## $ Temp3pm : num 21.8 24.3 23.2 26.5 29.7 28.9 24.6 25.5 30.2 28.2 ...
## $ RainToday : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 2 ...
## $ RainTomorrow : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 2 1 ...dim(data)## [1] 145460 23Suppression des variables inutiles : Evaporation, Sunshine, Cloud9am, Cloud3pm
Suppresion des variables liées au vent
data = data[, -c(6, 7, 8, 9, 10, 11, 12, 13, 18, 19)]
head(data)## Date Location MinTemp MaxTemp Rainfall Humidity9am Humidity3pm
## 1 2008-12-01 Albury 13.4 22.9 0.6 71 22
## 2 2008-12-02 Albury 7.4 25.1 0.0 44 25
## 3 2008-12-03 Albury 12.9 25.7 0.0 38 30
## 4 2008-12-04 Albury 9.2 28.0 0.0 45 16
## 5 2008-12-05 Albury 17.5 32.3 1.0 82 33
## 6 2008-12-06 Albury 14.6 29.7 0.2 55 23
## Pressure9am Pressure3pm Temp9am Temp3pm RainToday RainTomorrow
## 1 1007.7 1007.1 16.9 21.8 No No
## 2 1010.6 1007.8 17.2 24.3 No No
## 3 1007.6 1008.7 21.0 23.2 No No
## 4 1017.6 1012.8 18.1 26.5 No No
## 5 1010.8 1006.0 17.8 29.7 No No
## 6 1009.2 1005.4 20.6 28.9 No Nodata=data[!(rowSums(is.na(data))),] #On supprime les NA
str(data)## 'data.frame': 124273 obs. of 13 variables:
## $ Date : Factor w/ 3436 levels "2007-11-01","2007-11-02",..: 397 398 399 400 401 402 403 404 405 406 ...
## $ Location : Factor w/ 49 levels "Adelaide","Albany",..: 3 3 3 3 3 3 3 3 3 3 ...
## $ MinTemp : num 13.4 7.4 12.9 9.2 17.5 14.6 14.3 7.7 9.7 13.1 ...
## $ MaxTemp : num 22.9 25.1 25.7 28 32.3 29.7 25 26.7 31.9 30.1 ...
## $ Rainfall : num 0.6 0 0 0 1 0.2 0 0 0 1.4 ...
## $ Humidity9am : int 71 44 38 45 82 55 49 48 42 58 ...
## $ Humidity3pm : int 22 25 30 16 33 23 19 19 9 27 ...
## $ Pressure9am : num 1008 1011 1008 1018 1011 ...
## $ Pressure3pm : num 1007 1008 1009 1013 1006 ...
## $ Temp9am : num 16.9 17.2 21 18.1 17.8 20.6 18.1 16.3 18.3 20.1 ...
## $ Temp3pm : num 21.8 24.3 23.2 26.5 29.7 28.9 24.6 25.5 30.2 28.2 ...
## $ RainToday : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 1 2 ...
## $ RainTomorrow: Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 1 1 2 1 ...attach(data)
dim(data)## [1] 124273 13head(data)## Date Location MinTemp MaxTemp Rainfall Humidity9am Humidity3pm
## 1 2008-12-01 Albury 13.4 22.9 0.6 71 22
## 2 2008-12-02 Albury 7.4 25.1 0.0 44 25
## 3 2008-12-03 Albury 12.9 25.7 0.0 38 30
## 4 2008-12-04 Albury 9.2 28.0 0.0 45 16
## 5 2008-12-05 Albury 17.5 32.3 1.0 82 33
## 6 2008-12-06 Albury 14.6 29.7 0.2 55 23
## Pressure9am Pressure3pm Temp9am Temp3pm RainToday RainTomorrow
## 1 1007.7 1007.1 16.9 21.8 No No
## 2 1010.6 1007.8 17.2 24.3 No No
## 3 1007.6 1008.7 21.0 23.2 No No
## 4 1017.6 1012.8 18.1 26.5 No No
## 5 1010.8 1006.0 17.8 29.7 No No
## 6 1009.2 1005.4 20.6 28.9 No NoAjout des variables Year, Month, Température moyenne
data <- mutate(data, Date = as.Date(Date))
data = data %>% mutate(Year = year(Date),
AvgTemp = (MaxTemp + MinTemp)/2)Suppresion de la variable Date
data = data[, -1]
head(data)## Location MinTemp MaxTemp Rainfall Humidity9am Humidity3pm Pressure9am
## 1 Albury 13.4 22.9 0.6 71 22 1007.7
## 2 Albury 7.4 25.1 0.0 44 25 1010.6
## 3 Albury 12.9 25.7 0.0 38 30 1007.6
## 4 Albury 9.2 28.0 0.0 45 16 1017.6
## 5 Albury 17.5 32.3 1.0 82 33 1010.8
## 6 Albury 14.6 29.7 0.2 55 23 1009.2
## Pressure3pm Temp9am Temp3pm RainToday RainTomorrow Year AvgTemp
## 1 1007.1 16.9 21.8 No No 2008 18.15
## 2 1007.8 17.2 24.3 No No 2008 16.25
## 3 1008.7 21.0 23.2 No No 2008 19.30
## 4 1012.8 18.1 26.5 No No 2008 18.60
## 5 1006.0 17.8 29.7 No No 2008 24.90
## 6 1005.4 20.6 28.9 No No 2008 22.15# Group by les lignes par location et par année
by_loca <- data %>% group_by(Location, Year)
head(by_loca)## # A tibble: 6 x 14
## # Groups: Location, Year [1]
## Location MinTemp MaxTemp Rainfall Humidity9am Humidity3pm Pressure9am
## <fct> <dbl> <dbl> <dbl> <int> <int> <dbl>
## 1 Albury 13.4 22.9 0.6 71 22 1008.
## 2 Albury 7.4 25.1 0 44 25 1011.
## 3 Albury 12.9 25.7 0 38 30 1008.
## 4 Albury 9.2 28 0 45 16 1018.
## 5 Albury 17.5 32.3 1 82 33 1011.
## 6 Albury 14.6 29.7 0.2 55 23 1009.
## # … with 7 more variables: Pressure3pm <dbl>, Temp9am <dbl>, Temp3pm <dbl>,
## # RainToday <fct>, RainTomorrow <fct>, Year <dbl>, AvgTemp <dbl># Extraire 2300 lignes pour chaque ville
by_year = by_loca %>% filter(Year >= 2010 & Year <= 2017)
data_year<- by_year %>% group_by(Location)
data_year = data_year %>% filter(n() > 2300)
data_year <- data_year %>% slice(1:2300)On veut étudier Sydney, Sydney est le 19e ville dans la base
On supprime la variable Location, car il n’y en a plus besoin.
dataReady = data_year[(19*2300+1):(20*2300),]
data = dataReady[, -c(1, 11, 12, 13)]
head(data)## # A tibble: 6 x 10
## MinTemp MaxTemp Rainfall Humidity9am Humidity3pm Pressure9am Pressure3pm
## <dbl> <dbl> <dbl> <int> <int> <dbl> <dbl>
## 1 18.6 24.5 0 53 55 1022. 1020.
## 2 19.3 25.2 0 77 73 1019. 1018.
## 3 20.7 26.4 0 73 70 1017. 1015.
## 4 20.2 26.7 0 70 65 1015. 1015
## 5 20.9 24.7 0 85 79 1018. 1017.
## 6 19.5 24.9 0.8 82 68 1019. 1018.
## # … with 3 more variables: Temp9am <dbl>, Temp3pm <dbl>, AvgTemp <dbl>summary(data)## MinTemp MaxTemp Rainfall Humidity9am
## Min. : 9.40 Min. :15.20 Min. : 0.000 Min. :40.00
## 1st Qu.:14.60 1st Qu.:19.50 1st Qu.: 0.000 1st Qu.:62.00
## Median :16.70 Median :21.50 Median : 0.200 Median :70.00
## Mean :16.83 Mean :21.75 Mean : 3.303 Mean :71.03
## 3rd Qu.:19.00 3rd Qu.:24.00 3rd Qu.: 1.800 3rd Qu.:80.00
## Max. :23.80 Max. :28.40 Max. :156.800 Max. :99.00
## Humidity3pm Pressure9am Pressure3pm Temp9am
## Min. :43.00 Min. : 994.6 Min. : 995.2 Min. :12.20
## 1st Qu.:59.00 1st Qu.:1014.2 1st Qu.:1012.5 1st Qu.:17.60
## Median :66.00 Median :1018.0 Median :1016.3 Median :19.60
## Mean :67.94 Mean :1017.7 Mean :1015.9 Mean :19.68
## 3rd Qu.:76.00 3rd Qu.:1021.6 3rd Qu.:1019.8 3rd Qu.:21.90
## Max. :98.00 Max. :1033.0 Max. :1030.6 Max. :25.90
## Temp3pm AvgTemp
## Min. :12.30 Min. :12.85
## 1st Qu.:18.20 1st Qu.:17.05
## Median :20.20 Median :19.15
## Mean :20.41 Mean :19.29
## 3rd Qu.:22.70 3rd Qu.:21.50
## Max. :27.60 Max. :25.95pairs(data)
On peut par exemple dire que MinTemp, MaxTemp, Temp9am,Temp3pm sont fortement corrélées.
CAH
Les variables étant dans des unités différentes, on va travailler sur les données centrées réduites pour accorder la même importance à chaque variable et éviter que les variables à forte variance pèsent indûment sur les résultats.
data.cr <- scale(data,center=TRUE, scale=TRUE)
d.data.cr <- dist(data.cr)On utilise la mesure de Ward :
cah.ward <- hclust(d.data.cr, method="ward.D2")On affichage le dendrogramme :
plot(cah.ward, hang=-1, cex=0.2) 
Nombre de classes ?
Au vu du dendogramme, on va garder 4 ou 5 groupes car après les hauteurs des branches deviennent trop grandes (à l’oeil, on peut voir les paquets qui se détachent).
cah.ward$height## [1] 0.1720470 0.1735135 0.2019882 0.2198837 0.2601319 0.2675723
## [7] 0.2700539 0.2721642 0.2815944 0.2847263 0.2849398 0.2856560
## [13] 0.2869685 0.2896164 0.2975261 0.3090859 0.3124122 0.3134786
## [19] 0.3138778 0.3247142 0.3266595 0.3284561 0.3292599 0.3333532
## [25] 0.3350805 0.3364034 0.3368516 0.3370509 0.3440252 0.3449398
## [31] 0.3497932 0.3498577 0.3507893 0.3519389 0.3523627 0.3524819
## [37] 0.3528658 0.3546680 0.3547867 0.3564216 0.3576374 0.3588995
## [43] 0.3613034 0.3623132 0.3633976 0.3633998 0.3638541 0.3650293
## [49] 0.3654436 0.3658112 0.3682339 0.3683429 0.3695007 0.3715995
## [55] 0.3732332 0.3732457 0.3758313 0.3767916 0.3771826 0.3800750
## [61] 0.3802412 0.3802937 0.3823888 0.3823895 0.3828453 0.3834189
## [67] 0.3835290 0.3845728 0.3864617 0.3868611 0.3876287 0.3880659
## [73] 0.3890057 0.3890980 0.3895242 0.3906030 0.3919888 0.3922950
## [79] 0.3924371 0.3947844 0.3962240 0.3967517 0.3980867 0.3989136
## [85] 0.3991227 0.3992138 0.3993459 0.4017529 0.4022123 0.4037235
## [91] 0.4041087 0.4045324 0.4051403 0.4051725 0.4054617 0.4067941
## [97] 0.4072660 0.4093158 0.4099564 0.4100987 0.4103294 0.4115082
## [103] 0.4119159 0.4135228 0.4137044 0.4148639 0.4149599 0.4155208
## [109] 0.4160685 0.4169124 0.4171388 0.4172651 0.4180689 0.4182121
## [115] 0.4187681 0.4188882 0.4209349 0.4219046 0.4221267 0.4243690
## [121] 0.4259638 0.4268699 0.4269590 0.4278693 0.4279679 0.4291089
## [127] 0.4291926 0.4292998 0.4302205 0.4319197 0.4326601 0.4334122
## [133] 0.4337554 0.4345631 0.4350402 0.4353796 0.4356568 0.4368666
## [139] 0.4369060 0.4370367 0.4372001 0.4377558 0.4380535 0.4382367
## [145] 0.4397510 0.4400134 0.4404138 0.4409362 0.4439034 0.4441977
## [151] 0.4454192 0.4459776 0.4470017 0.4471570 0.4473739 0.4474556
## [157] 0.4475645 0.4486333 0.4490140 0.4493833 0.4494033 0.4497146
## [163] 0.4511539 0.4512780 0.4519098 0.4528240 0.4533498 0.4540529
## [169] 0.4547670 0.4549975 0.4551278 0.4556033 0.4566493 0.4571964
## [175] 0.4584089 0.4587951 0.4590453 0.4598858 0.4607303 0.4608520
## [181] 0.4614549 0.4616821 0.4622137 0.4625909 0.4637698 0.4638133
## [187] 0.4640091 0.4649149 0.4655885 0.4659579 0.4673668 0.4677393
## [193] 0.4690459 0.4695276 0.4698176 0.4703435 0.4713175 0.4714483
## [199] 0.4715418 0.4719928 0.4722664 0.4724886 0.4743058 0.4749097
## [205] 0.4750390 0.4753467 0.4755180 0.4760173 0.4763130 0.4768197
## [211] 0.4768372 0.4775323 0.4775891 0.4783403 0.4788994 0.4792454
## [217] 0.4799429 0.4801259 0.4802442 0.4807249 0.4808738 0.4808953
## [223] 0.4810040 0.4810284 0.4811413 0.4825115 0.4832130 0.4835682
## [229] 0.4836931 0.4838133 0.4840054 0.4840291 0.4846821 0.4854952
## [235] 0.4858133 0.4858250 0.4859796 0.4861714 0.4867872 0.4868459
## [241] 0.4870232 0.4872153 0.4872940 0.4874943 0.4878586 0.4891645
## [247] 0.4894691 0.4906057 0.4906608 0.4907510 0.4909828 0.4912521
## [253] 0.4913634 0.4918643 0.4939948 0.4942741 0.4948892 0.4956883
## [259] 0.4958620 0.4963805 0.4963946 0.4966565 0.4968340 0.4972595
## [265] 0.4986964 0.4992471 0.4994401 0.4995992 0.4999551 0.5003051
## [271] 0.5011469 0.5014866 0.5015534 0.5020146 0.5022051 0.5024299
## [277] 0.5036959 0.5037361 0.5039559 0.5043724 0.5049153 0.5050556
## [283] 0.5050735 0.5057275 0.5061740 0.5072629 0.5078331 0.5081942
## [289] 0.5088786 0.5089670 0.5089825 0.5092293 0.5096174 0.5104516
## [295] 0.5104831 0.5105525 0.5108850 0.5117565 0.5137750 0.5138853
## [301] 0.5139168 0.5150949 0.5159271 0.5161933 0.5166669 0.5169594
## [307] 0.5177760 0.5177777 0.5197240 0.5209010 0.5219691 0.5230798
## [313] 0.5235443 0.5242876 0.5245316 0.5249533 0.5250793 0.5256978
## [319] 0.5267764 0.5281637 0.5287403 0.5291585 0.5292573 0.5299924
## [325] 0.5302307 0.5303293 0.5304301 0.5305454 0.5307147 0.5314701
## [331] 0.5316984 0.5319412 0.5325205 0.5333473 0.5340037 0.5342073
## [337] 0.5350581 0.5352681 0.5352742 0.5353913 0.5357974 0.5359789
## [343] 0.5364216 0.5375554 0.5378575 0.5381178 0.5382075 0.5388712
## [349] 0.5396812 0.5400154 0.5405008 0.5415133 0.5420501 0.5423900
## [355] 0.5437357 0.5437366 0.5443979 0.5445930 0.5450730 0.5458465
## [361] 0.5462779 0.5472794 0.5478320 0.5480793 0.5496510 0.5499766
## [367] 0.5502935 0.5504866 0.5505006 0.5505111 0.5512156 0.5517601
## [373] 0.5520516 0.5527569 0.5541879 0.5551790 0.5556946 0.5566856
## [379] 0.5582908 0.5592755 0.5596421 0.5603415 0.5606536 0.5607627
## [385] 0.5616991 0.5619940 0.5626323 0.5628597 0.5631373 0.5632752
## [391] 0.5633626 0.5637562 0.5639557 0.5641037 0.5641073 0.5642562
## [397] 0.5646278 0.5648792 0.5649092 0.5655445 0.5657308 0.5661559
## [403] 0.5663763 0.5669713 0.5670314 0.5670817 0.5675395 0.5677002
## [409] 0.5679579 0.5682146 0.5690487 0.5694279 0.5704550 0.5707574
## [415] 0.5711662 0.5728152 0.5729869 0.5735997 0.5740152 0.5749858
## [421] 0.5757448 0.5763547 0.5763754 0.5764903 0.5766049 0.5766483
## [427] 0.5778814 0.5781381 0.5783530 0.5790533 0.5790576 0.5795935
## [433] 0.5800595 0.5804845 0.5805716 0.5809323 0.5813397 0.5814221
## [439] 0.5820453 0.5822978 0.5823265 0.5824230 0.5830428 0.5834003
## [445] 0.5834422 0.5839208 0.5852485 0.5856622 0.5864159 0.5869482
## [451] 0.5875058 0.5883280 0.5888936 0.5890567 0.5898794 0.5900479
## [457] 0.5900811 0.5904486 0.5912619 0.5925459 0.5925503 0.5926218
## [463] 0.5928408 0.5929967 0.5930578 0.5931589 0.5942565 0.5943622
## [469] 0.5946798 0.5947566 0.5955459 0.5958344 0.5970810 0.5978248
## [475] 0.5979488 0.5980189 0.5986285 0.5987837 0.5989970 0.5991942
## [481] 0.5996818 0.6012273 0.6026977 0.6028101 0.6036655 0.6037686
## [487] 0.6037793 0.6043971 0.6057045 0.6059844 0.6068265 0.6069370
## [493] 0.6071993 0.6072429 0.6078185 0.6078396 0.6082642 0.6084317
## [499] 0.6084709 0.6093026 0.6100874 0.6101582 0.6101912 0.6120671
## [505] 0.6123505 0.6135468 0.6136606 0.6144772 0.6149056 0.6149129
## [511] 0.6150027 0.6152683 0.6156887 0.6158643 0.6162696 0.6163508
## [517] 0.6170226 0.6171641 0.6178025 0.6181326 0.6182480 0.6191734
## [523] 0.6196822 0.6203448 0.6204031 0.6208267 0.6218585 0.6219552
## [529] 0.6219964 0.6220917 0.6221632 0.6222702 0.6222736 0.6230694
## [535] 0.6231105 0.6234716 0.6238224 0.6240087 0.6255160 0.6260563
## [541] 0.6267204 0.6268092 0.6271448 0.6272539 0.6277706 0.6279162
## [547] 0.6282287 0.6283807 0.6288149 0.6288543 0.6290747 0.6290813
## [553] 0.6290851 0.6292470 0.6294951 0.6295094 0.6297444 0.6301531
## [559] 0.6310636 0.6311600 0.6319232 0.6321069 0.6321139 0.6323634
## [565] 0.6324723 0.6330740 0.6332367 0.6337600 0.6347275 0.6348634
## [571] 0.6359859 0.6363688 0.6365959 0.6369307 0.6371972 0.6373597
## [577] 0.6375979 0.6383095 0.6395948 0.6396201 0.6398157 0.6399707
## [583] 0.6407148 0.6407494 0.6414107 0.6414145 0.6417679 0.6464921
## [589] 0.6468493 0.6473786 0.6499946 0.6500850 0.6522767 0.6524527
## [595] 0.6530745 0.6532812 0.6539397 0.6547936 0.6550731 0.6557741
## [601] 0.6558859 0.6561392 0.6563774 0.6564890 0.6566702 0.6569562
## [607] 0.6570556 0.6571304 0.6571731 0.6574828 0.6576909 0.6578396
## [613] 0.6582966 0.6589668 0.6590079 0.6592026 0.6592760 0.6594312
## [619] 0.6598085 0.6598643 0.6600175 0.6601224 0.6605549 0.6607632
## [625] 0.6607775 0.6614931 0.6622284 0.6623421 0.6625877 0.6630426
## [631] 0.6634070 0.6636007 0.6638680 0.6645037 0.6645683 0.6646792
## [637] 0.6647822 0.6649450 0.6653527 0.6657818 0.6665917 0.6666693
## [643] 0.6666694 0.6670533 0.6672472 0.6676359 0.6683242 0.6684060
## [649] 0.6685801 0.6698160 0.6703558 0.6707486 0.6712143 0.6714618
## [655] 0.6715783 0.6722902 0.6724245 0.6729780 0.6731359 0.6732837
## [661] 0.6733428 0.6736430 0.6737178 0.6739161 0.6739849 0.6743818
## [667] 0.6744256 0.6745169 0.6752646 0.6760485 0.6761329 0.6762121
## [673] 0.6765666 0.6767281 0.6773006 0.6776340 0.6778213 0.6781997
## [679] 0.6784096 0.6787985 0.6789063 0.6790873 0.6804800 0.6805075
## [685] 0.6806905 0.6828364 0.6829118 0.6831741 0.6847412 0.6852247
## [691] 0.6874662 0.6878623 0.6882655 0.6889137 0.6889517 0.6893856
## [697] 0.6897498 0.6898005 0.6903260 0.6910015 0.6913858 0.6914827
## [703] 0.6924833 0.6926349 0.6932108 0.6940506 0.6941197 0.6943662
## [709] 0.6944098 0.6945250 0.6947297 0.6953701 0.6954768 0.6956493
## [715] 0.6957698 0.6964421 0.6977119 0.6996477 0.7007595 0.7013184
## [721] 0.7014812 0.7028200 0.7029957 0.7035111 0.7037445 0.7039246
## [727] 0.7040444 0.7043317 0.7047833 0.7054661 0.7055949 0.7056347
## [733] 0.7068715 0.7073508 0.7074637 0.7077110 0.7087836 0.7098421
## [739] 0.7101903 0.7111526 0.7114827 0.7124953 0.7131578 0.7135208
## [745] 0.7136413 0.7136564 0.7147591 0.7157803 0.7159525 0.7163795
## [751] 0.7164814 0.7165156 0.7166195 0.7167620 0.7171236 0.7176044
## [757] 0.7193216 0.7204757 0.7213360 0.7214573 0.7219203 0.7219808
## [763] 0.7223345 0.7233101 0.7238130 0.7239552 0.7260479 0.7260554
## [769] 0.7265269 0.7270687 0.7270819 0.7274054 0.7278557 0.7286287
## [775] 0.7292351 0.7297960 0.7307108 0.7314116 0.7315704 0.7315967
## [781] 0.7326208 0.7328390 0.7329917 0.7366144 0.7372214 0.7375794
## [787] 0.7377639 0.7381805 0.7383337 0.7383556 0.7385348 0.7398265
## [793] 0.7399820 0.7405464 0.7408120 0.7409964 0.7410111 0.7411708
## [799] 0.7412307 0.7417766 0.7418449 0.7425892 0.7426334 0.7427022
## [805] 0.7434729 0.7436950 0.7449410 0.7451874 0.7455157 0.7457445
## [811] 0.7457526 0.7459263 0.7461097 0.7470316 0.7473041 0.7473187
## [817] 0.7474035 0.7474061 0.7484093 0.7489785 0.7493281 0.7495657
## [823] 0.7497207 0.7500929 0.7503066 0.7520410 0.7527497 0.7527899
## [829] 0.7533940 0.7535343 0.7536037 0.7536737 0.7537319 0.7538011
## [835] 0.7538413 0.7538870 0.7541718 0.7541800 0.7551531 0.7554594
## [841] 0.7558550 0.7560256 0.7571993 0.7573526 0.7574973 0.7576225
## [847] 0.7582795 0.7584277 0.7585818 0.7592316 0.7593949 0.7594891
## [853] 0.7599164 0.7605026 0.7609557 0.7618434 0.7618756 0.7637994
## [859] 0.7643282 0.7651233 0.7652028 0.7656360 0.7657412 0.7658847
## [865] 0.7670805 0.7671554 0.7679937 0.7682854 0.7683725 0.7685994
## [871] 0.7694849 0.7694940 0.7698605 0.7701457 0.7707251 0.7715425
## [877] 0.7724837 0.7730683 0.7738784 0.7746644 0.7748349 0.7749892
## [883] 0.7750304 0.7750390 0.7751741 0.7764139 0.7764205 0.7779722
## [889] 0.7783211 0.7787744 0.7793399 0.7796585 0.7800115 0.7800367
## [895] 0.7801465 0.7812219 0.7829069 0.7830044 0.7833641 0.7834737
## [901] 0.7838130 0.7841026 0.7867847 0.7886151 0.7896421 0.7906656
## [907] 0.7909752 0.7920344 0.7925415 0.7931039 0.7936289 0.7940073
## [913] 0.7941960 0.7942207 0.7943376 0.7945351 0.7949089 0.7950589
## [919] 0.7954381 0.7959382 0.7968087 0.7983656 0.7988792 0.8002204
## [925] 0.8004623 0.8012656 0.8017529 0.8020776 0.8021792 0.8030062
## [931] 0.8038735 0.8044499 0.8047333 0.8052833 0.8061435 0.8070430
## [937] 0.8073446 0.8074020 0.8077862 0.8086956 0.8092365 0.8092485
## [943] 0.8093043 0.8104545 0.8105970 0.8117159 0.8122833 0.8129451
## [949] 0.8130414 0.8131405 0.8132601 0.8133188 0.8140390 0.8144882
## [955] 0.8149419 0.8149925 0.8159958 0.8162729 0.8175117 0.8177298
## [961] 0.8179039 0.8179791 0.8184564 0.8188923 0.8193312 0.8195626
## [967] 0.8199032 0.8201534 0.8202064 0.8202353 0.8206214 0.8213134
## [973] 0.8216586 0.8221469 0.8221767 0.8231532 0.8234968 0.8244505
## [979] 0.8262599 0.8266728 0.8269204 0.8271919 0.8282918 0.8283330
## [985] 0.8287709 0.8287968 0.8289144 0.8292146 0.8294321 0.8294498
## [991] 0.8303896 0.8307441 0.8307683 0.8313645 0.8316558 0.8322682
## [997] 0.8324496 0.8331097 0.8338075 0.8343683 0.8347659 0.8364015
## [1003] 0.8364800 0.8370371 0.8376577 0.8381507 0.8407316 0.8447110
## [1009] 0.8447255 0.8453770 0.8455298 0.8468037 0.8471627 0.8472286
## [1015] 0.8478946 0.8480085 0.8497094 0.8504785 0.8508322 0.8529298
## [1021] 0.8533119 0.8534380 0.8539122 0.8540821 0.8541645 0.8549627
## [1027] 0.8560053 0.8573821 0.8587681 0.8588455 0.8598208 0.8599371
## [1033] 0.8601054 0.8602344 0.8616748 0.8619009 0.8621112 0.8627906
## [1039] 0.8628122 0.8635418 0.8646582 0.8656309 0.8660176 0.8668410
## [1045] 0.8679619 0.8697297 0.8697472 0.8697968 0.8698365 0.8700123
## [1051] 0.8700650 0.8705890 0.8710329 0.8726448 0.8732383 0.8732817
## [1057] 0.8742390 0.8754162 0.8760416 0.8771325 0.8771905 0.8784774
## [1063] 0.8786810 0.8791307 0.8795107 0.8803549 0.8818419 0.8819313
## [1069] 0.8828674 0.8831068 0.8832272 0.8839057 0.8839430 0.8844095
## [1075] 0.8865652 0.8873162 0.8876094 0.8876097 0.8879364 0.8880269
## [1081] 0.8894016 0.8902534 0.8903489 0.8908086 0.8929190 0.8945545
## [1087] 0.8950292 0.8954016 0.8961583 0.8964922 0.8969051 0.8969787
## [1093] 0.8977710 0.8979557 0.8979898 0.8980390 0.8991128 0.9000252
## [1099] 0.9007652 0.9008054 0.9014428 0.9014642 0.9027737 0.9032069
## [1105] 0.9035311 0.9046027 0.9050126 0.9054103 0.9054456 0.9054959
## [1111] 0.9062094 0.9066786 0.9071990 0.9084307 0.9100115 0.9114225
## [1117] 0.9147136 0.9147482 0.9147567 0.9151964 0.9154164 0.9176975
## [1123] 0.9191865 0.9192542 0.9199036 0.9223626 0.9228028 0.9264187
## [1129] 0.9277507 0.9288620 0.9300858 0.9300930 0.9308648 0.9317625
## [1135] 0.9318011 0.9323545 0.9341834 0.9346445 0.9346497 0.9348797
## [1141] 0.9350591 0.9363101 0.9372962 0.9374483 0.9375062 0.9378156
## [1147] 0.9381002 0.9390691 0.9403512 0.9406167 0.9419768 0.9439814
## [1153] 0.9458320 0.9461854 0.9463323 0.9470196 0.9476587 0.9482092
## [1159] 0.9483598 0.9484787 0.9484864 0.9500165 0.9508692 0.9509736
## [1165] 0.9510580 0.9511175 0.9516131 0.9543279 0.9545429 0.9547443
## [1171] 0.9554912 0.9563161 0.9577317 0.9582201 0.9583789 0.9592188
## [1177] 0.9596947 0.9601905 0.9601923 0.9608883 0.9611581 0.9614579
## [1183] 0.9624915 0.9630935 0.9645697 0.9645921 0.9655337 0.9655774
## [1189] 0.9658942 0.9664572 0.9679634 0.9707428 0.9715779 0.9718427
## [1195] 0.9721034 0.9721131 0.9730049 0.9731113 0.9738585 0.9738784
## [1201] 0.9749304 0.9758571 0.9763416 0.9778621 0.9781126 0.9792017
## [1207] 0.9792169 0.9798268 0.9804299 0.9804722 0.9807982 0.9814008
## [1213] 0.9815395 0.9824445 0.9827863 0.9829542 0.9831671 0.9832184
## [1219] 0.9839800 0.9841682 0.9844787 0.9846993 0.9861015 0.9871999
## [1225] 0.9872320 0.9890139 0.9891864 0.9911653 0.9913988 0.9919343
## [1231] 0.9922498 0.9930176 0.9939195 0.9941734 0.9943025 0.9965391
## [1237] 0.9966786 0.9988840 0.9990466 0.9992926 1.0003026 1.0021116
## [1243] 1.0030468 1.0047025 1.0054915 1.0057376 1.0065163 1.0067643
## [1249] 1.0067699 1.0072598 1.0083161 1.0087018 1.0098236 1.0104439
## [1255] 1.0112747 1.0115052 1.0128923 1.0136669 1.0141601 1.0145871
## [1261] 1.0145897 1.0147240 1.0147376 1.0156779 1.0157732 1.0167663
## [1267] 1.0183310 1.0187734 1.0198151 1.0198519 1.0203721 1.0222429
## [1273] 1.0229554 1.0230696 1.0233197 1.0235946 1.0241707 1.0255577
## [1279] 1.0270338 1.0277699 1.0297738 1.0300100 1.0300459 1.0304098
## [1285] 1.0305522 1.0308853 1.0324743 1.0330723 1.0333103 1.0338815
## [1291] 1.0347292 1.0348075 1.0349140 1.0357268 1.0359398 1.0374703
## [1297] 1.0377482 1.0388364 1.0392213 1.0405074 1.0430246 1.0441164
## [1303] 1.0449127 1.0455850 1.0460215 1.0466317 1.0467116 1.0469027
## [1309] 1.0481177 1.0488440 1.0497110 1.0517261 1.0520642 1.0555481
## [1315] 1.0574452 1.0578468 1.0580621 1.0595243 1.0608892 1.0614195
## [1321] 1.0619367 1.0626534 1.0627080 1.0627990 1.0628534 1.0631119
## [1327] 1.0635883 1.0643174 1.0648992 1.0650121 1.0661107 1.0672341
## [1333] 1.0678749 1.0680066 1.0697864 1.0741863 1.0748755 1.0749784
## [1339] 1.0763685 1.0769091 1.0792139 1.0800708 1.0806208 1.0812567
## [1345] 1.0817457 1.0818835 1.0819152 1.0819546 1.0820133 1.0823307
## [1351] 1.0840158 1.0849023 1.0853968 1.0861082 1.0861628 1.0864227
## [1357] 1.0869858 1.0874022 1.0886233 1.0890866 1.0904448 1.0919304
## [1363] 1.0937159 1.0950022 1.0952554 1.0957835 1.0964840 1.0979811
## [1369] 1.0987403 1.0992247 1.0992315 1.1000039 1.1002391 1.1013775
## [1375] 1.1026304 1.1027366 1.1028884 1.1042691 1.1043195 1.1055237
## [1381] 1.1086549 1.1131017 1.1138909 1.1151416 1.1152046 1.1174117
## [1387] 1.1174186 1.1177210 1.1183843 1.1185025 1.1213730 1.1247056
## [1393] 1.1257261 1.1262225 1.1292490 1.1298665 1.1309039 1.1322571
## [1399] 1.1328745 1.1330408 1.1347715 1.1349432 1.1353753 1.1358820
## [1405] 1.1364431 1.1386272 1.1387587 1.1403302 1.1404228 1.1420097
## [1411] 1.1441132 1.1463518 1.1466089 1.1475143 1.1475730 1.1492941
## [1417] 1.1503238 1.1516628 1.1519296 1.1525550 1.1533898 1.1546714
## [1423] 1.1555424 1.1555453 1.1565593 1.1566682 1.1573865 1.1581806
## [1429] 1.1584128 1.1614027 1.1614269 1.1622568 1.1637738 1.1650323
## [1435] 1.1653463 1.1656880 1.1678587 1.1683905 1.1690676 1.1699073
## [1441] 1.1706660 1.1715697 1.1718249 1.1723033 1.1728936 1.1730046
## [1447] 1.1732179 1.1735953 1.1739925 1.1745378 1.1771560 1.1775441
## [1453] 1.1780537 1.1797450 1.1820034 1.1844041 1.1854435 1.1868073
## [1459] 1.1873928 1.1878781 1.1893119 1.1901639 1.1903660 1.1912268
## [1465] 1.1922176 1.1926333 1.1927902 1.1938147 1.1962577 1.1981495
## [1471] 1.1985143 1.1985592 1.1990461 1.1991275 1.1995200 1.1999519
## [1477] 1.2014258 1.2020362 1.2038118 1.2041783 1.2059218 1.2072504
## [1483] 1.2083849 1.2084293 1.2087268 1.2099515 1.2117004 1.2124104
## [1489] 1.2128650 1.2136927 1.2147264 1.2161839 1.2163150 1.2200792
## [1495] 1.2213760 1.2215103 1.2222150 1.2224025 1.2232022 1.2232602
## [1501] 1.2237422 1.2244234 1.2246315 1.2258755 1.2263274 1.2272824
## [1507] 1.2274066 1.2275329 1.2295792 1.2307251 1.2324780 1.2360625
## [1513] 1.2369252 1.2373274 1.2374776 1.2382874 1.2398477 1.2416535
## [1519] 1.2424545 1.2436524 1.2458027 1.2467566 1.2484418 1.2490162
## [1525] 1.2495251 1.2523647 1.2548452 1.2554274 1.2555548 1.2562986
## [1531] 1.2565529 1.2572272 1.2579633 1.2613796 1.2633257 1.2635152
## [1537] 1.2643135 1.2648953 1.2650368 1.2661860 1.2666744 1.2687481
## [1543] 1.2709757 1.2735285 1.2736494 1.2756235 1.2772494 1.2781034
## [1549] 1.2785381 1.2795886 1.2800241 1.2800406 1.2817326 1.2819541
## [1555] 1.2829440 1.2859882 1.2860742 1.2869872 1.2883833 1.2892867
## [1561] 1.2898550 1.2917478 1.2924151 1.2925132 1.2952029 1.2977750
## [1567] 1.2980554 1.3005139 1.3006650 1.3007460 1.3009317 1.3019108
## [1573] 1.3029487 1.3037416 1.3049984 1.3058234 1.3063048 1.3067561
## [1579] 1.3086955 1.3154814 1.3157941 1.3165069 1.3167836 1.3179420
## [1585] 1.3183128 1.3198638 1.3210494 1.3269609 1.3287206 1.3318451
## [1591] 1.3342740 1.3349397 1.3355628 1.3356592 1.3366280 1.3408722
## [1597] 1.3429692 1.3432889 1.3442026 1.3450673 1.3454883 1.3455432
## [1603] 1.3481846 1.3500621 1.3508930 1.3554631 1.3589260 1.3620920
## [1609] 1.3636627 1.3649376 1.3651556 1.3686199 1.3696722 1.3713594
## [1615] 1.3732902 1.3735053 1.3772325 1.3784412 1.3795371 1.3795942
## [1621] 1.3814474 1.3829251 1.3838569 1.3846428 1.3857183 1.3897211
## [1627] 1.3901185 1.3903952 1.3914051 1.3919411 1.3954015 1.3960868
## [1633] 1.3961494 1.4018472 1.4021056 1.4039238 1.4085773 1.4089678
## [1639] 1.4101737 1.4118522 1.4121592 1.4126702 1.4130630 1.4131667
## [1645] 1.4138053 1.4157711 1.4178521 1.4187727 1.4195717 1.4199811
## [1651] 1.4233572 1.4236697 1.4253488 1.4259968 1.4260486 1.4267522
## [1657] 1.4275042 1.4295438 1.4309956 1.4321371 1.4330809 1.4399243
## [1663] 1.4407096 1.4418439 1.4427453 1.4432190 1.4437418 1.4438016
## [1669] 1.4456521 1.4456730 1.4487773 1.4498902 1.4509150 1.4523621
## [1675] 1.4534811 1.4570276 1.4626462 1.4716815 1.4720143 1.4727136
## [1681] 1.4750172 1.4752694 1.4763282 1.4774566 1.4800187 1.4813485
## [1687] 1.4820112 1.4834483 1.4851707 1.4860584 1.4864585 1.4867025
## [1693] 1.4890042 1.4920782 1.4931229 1.4933747 1.4951437 1.4965059
## [1699] 1.5008830 1.5011818 1.5018938 1.5025491 1.5028357 1.5030821
## [1705] 1.5056858 1.5062979 1.5071564 1.5103364 1.5111724 1.5113727
## [1711] 1.5127681 1.5133059 1.5138474 1.5180594 1.5190044 1.5228436
## [1717] 1.5262343 1.5295433 1.5303003 1.5306857 1.5332281 1.5376315
## [1723] 1.5394887 1.5422913 1.5451451 1.5453773 1.5465554 1.5469524
## [1729] 1.5492449 1.5512944 1.5521963 1.5584811 1.5606261 1.5606598
## [1735] 1.5617033 1.5655089 1.5669691 1.5674678 1.5678869 1.5683463
## [1741] 1.5735705 1.5748865 1.5758837 1.5776904 1.5827061 1.5829671
## [1747] 1.5853224 1.6003652 1.6006164 1.6010863 1.6020551 1.6042015
## [1753] 1.6052779 1.6082992 1.6121857 1.6209937 1.6238177 1.6238344
## [1759] 1.6238996 1.6241730 1.6250326 1.6251262 1.6256465 1.6286073
## [1765] 1.6293859 1.6308965 1.6314172 1.6315983 1.6344405 1.6367661
## [1771] 1.6411350 1.6431842 1.6432949 1.6447440 1.6501074 1.6504058
## [1777] 1.6507636 1.6528441 1.6560412 1.6577178 1.6581265 1.6597456
## [1783] 1.6607213 1.6609102 1.6661388 1.6663671 1.6691407 1.6696525
## [1789] 1.6721620 1.6820360 1.6846066 1.6865434 1.6889176 1.6930991
## [1795] 1.6984720 1.7008520 1.7016805 1.7096092 1.7136466 1.7157790
## [1801] 1.7165590 1.7175880 1.7271617 1.7275531 1.7285506 1.7389740
## [1807] 1.7454352 1.7523719 1.7534853 1.7585402 1.7585604 1.7588329
## [1813] 1.7694932 1.7776066 1.7795162 1.7812217 1.7819125 1.7875866
## [1819] 1.7889339 1.7899365 1.7901456 1.7944671 1.7948225 1.7955777
## [1825] 1.7975224 1.7981327 1.8002356 1.8024061 1.8059971 1.8080864
## [1831] 1.8155705 1.8180895 1.8236906 1.8260580 1.8274076 1.8275148
## [1837] 1.8350814 1.8397183 1.8404805 1.8406855 1.8455768 1.8515209
## [1843] 1.8551967 1.8559672 1.8610174 1.8624208 1.8645605 1.8657388
## [1849] 1.8665972 1.8677048 1.8698392 1.8700164 1.8729554 1.8771517
## [1855] 1.8775915 1.8781755 1.8794078 1.8801192 1.8803785 1.8866979
## [1861] 1.8893232 1.8915454 1.8934853 1.8951396 1.8987542 1.8992750
## [1867] 1.9102980 1.9121268 1.9133796 1.9160454 1.9175789 1.9178513
## [1873] 1.9214565 1.9217978 1.9253228 1.9261299 1.9272068 1.9281402
## [1879] 1.9313350 1.9316360 1.9361894 1.9384404 1.9414024 1.9484093
## [1885] 1.9536026 1.9545779 1.9581116 1.9594009 1.9627919 1.9638633
## [1891] 1.9777290 1.9790932 1.9816245 1.9829934 1.9888067 1.9899495
## [1897] 2.0024603 2.0036402 2.0065323 2.0069631 2.0088237 2.0115375
## [1903] 2.0155715 2.0171262 2.0191473 2.0201080 2.0234297 2.0261072
## [1909] 2.0438230 2.0567678 2.0636313 2.0658300 2.0677668 2.0689835
## [1915] 2.0692007 2.0700957 2.0713258 2.0866379 2.0883402 2.0927396
## [1921] 2.0969616 2.1047230 2.1055757 2.1100394 2.1139683 2.1147829
## [1927] 2.1155144 2.1204372 2.1258424 2.1311731 2.1330866 2.1400710
## [1933] 2.1417963 2.1420682 2.1448374 2.1462064 2.1480565 2.1496460
## [1939] 2.1511025 2.1547767 2.1551235 2.1565596 2.1643176 2.1649402
## [1945] 2.1676541 2.1693250 2.1767428 2.1793480 2.1867110 2.1992557
## [1951] 2.2083865 2.2106034 2.2131498 2.2200281 2.2217600 2.2286257
## [1957] 2.2298974 2.2390440 2.2393015 2.2418520 2.2448694 2.2476892
## [1963] 2.2481490 2.2642734 2.2877960 2.2970873 2.2995314 2.3124699
## [1969] 2.3161273 2.3175565 2.3402208 2.3454942 2.3591721 2.3594162
## [1975] 2.3607938 2.3629115 2.3636761 2.3734334 2.3735555 2.3834169
## [1981] 2.3853514 2.3861121 2.3876009 2.3966971 2.3996039 2.4085088
## [1987] 2.4167299 2.4172439 2.4174765 2.4175322 2.4202989 2.4239986
## [1993] 2.4318210 2.4372540 2.4428654 2.4526638 2.4836319 2.4878418
## [1999] 2.4997693 2.5047015 2.5060349 2.5111601 2.5205294 2.5247558
## [2005] 2.5382656 2.5398301 2.5435299 2.5456429 2.5486967 2.5519215
## [2011] 2.5552796 2.5558080 2.5588329 2.5599484 2.5621150 2.5640541
## [2017] 2.5680290 2.5726923 2.5763707 2.5765995 2.5814477 2.5919966
## [2023] 2.5949313 2.5989147 2.6104946 2.6137039 2.6233350 2.6244647
## [2029] 2.6249021 2.6265465 2.6392170 2.6407169 2.6573517 2.6599641
## [2035] 2.6777222 2.6791668 2.6814275 2.6817859 2.6843435 2.6848772
## [2041] 2.6866188 2.6908301 2.7138315 2.7144258 2.7248559 2.7301569
## [2047] 2.7359845 2.7486347 2.7580230 2.7687816 2.7773295 2.7862940
## [2053] 2.7924538 2.8149050 2.8184045 2.8206959 2.8260915 2.8378468
## [2059] 2.8420757 2.8432878 2.8459755 2.8570101 2.8604739 2.8642130
## [2065] 2.8653104 2.8852788 2.9007960 2.9186248 2.9423761 2.9517922
## [2071] 2.9636901 2.9655866 2.9725784 2.9826863 2.9910800 2.9932650
## [2077] 3.0103506 3.0244801 3.0303243 3.0382426 3.0415988 3.0429840
## [2083] 3.0574260 3.0867455 3.0933206 3.1140658 3.1225182 3.1227603
## [2089] 3.1241297 3.1311504 3.1460197 3.1517578 3.1630106 3.1637972
## [2095] 3.1767311 3.1796823 3.1949022 3.1995226 3.2121238 3.2165786
## [2101] 3.2183231 3.2201877 3.2474577 3.2489856 3.2521060 3.2592743
## [2107] 3.2662510 3.2825903 3.2894529 3.2913257 3.2949023 3.2969356
## [2113] 3.2970257 3.3013525 3.3247556 3.3249054 3.3679460 3.3863611
## [2119] 3.3996622 3.4001593 3.4124408 3.4178616 3.4489398 3.4652033
## [2125] 3.4765205 3.4794751 3.5188086 3.5266922 3.5455007 3.5491084
## [2131] 3.5542591 3.5876405 3.6135678 3.6338087 3.6677072 3.6752350
## [2137] 3.6843044 3.6961164 3.6993319 3.7036778 3.7240977 3.7246246
## [2143] 3.7820345 3.7903513 3.7930644 3.7939586 3.7990345 3.8156025
## [2149] 3.8156793 3.8306291 3.8371117 3.8726525 3.8729742 3.8775006
## [2155] 3.8819237 3.8866782 3.9279117 3.9936977 4.0178850 4.0365251
## [2161] 4.0499507 4.0613106 4.0669474 4.0840432 4.1146182 4.1193782
## [2167] 4.1729019 4.2271076 4.2302465 4.2354411 4.2492793 4.2643778
## [2173] 4.2727063 4.3033916 4.3041744 4.3398677 4.3461774 4.3514905
## [2179] 4.3802115 4.4025093 4.4221213 4.4374787 4.4391075 4.4712035
## [2185] 4.4939646 4.5750358 4.5975297 4.7294520 4.7618201 4.7985029
## [2191] 4.8181275 4.8504575 4.8798306 4.8998115 4.9213187 4.9251375
## [2197] 4.9552067 5.0291743 5.0587383 5.0815809 5.0872854 5.1003976
## [2203] 5.1389420 5.1558399 5.1579564 5.1796469 5.3312483 5.3626316
## [2209] 5.3817887 5.4241578 5.4577165 5.4582250 5.4777764 5.4791407
## [2215] 5.5094493 5.6939869 5.6988444 5.7720164 5.7945188 5.8877661
## [2221] 5.9441077 5.9754978 6.0717683 6.0918880 6.1196793 6.1946549
## [2227] 6.2017318 6.2851962 6.3067197 6.3193443 6.3565358 6.4255585
## [2233] 6.4431615 6.4715959 6.6737212 6.8952237 7.0042314 7.0068910
## [2239] 7.1340845 7.1359970 7.3611680 7.4225371 7.5383580 7.5712922
## [2245] 7.5905989 7.6278969 7.9200891 7.9386557 7.9428632 7.9451998
## [2251] 7.9569757 8.1446161 8.1870313 8.4801644 8.5712445 8.5963497
## [2257] 8.6276438 8.7299346 9.0349994 9.2191881 9.8431754 9.8464939
## [2263] 9.8882455 9.9455643 10.2633079 10.3475786 10.4305757 10.6420559
## [2269] 10.6769504 10.7640623 11.9378255 12.3592579 12.3779762 13.5066361
## [2275] 13.7367796 14.2823862 14.5924310 14.6799347 15.3261713 16.1518716
## [2281] 17.0079064 17.0125443 17.2269594 18.3323575 19.2685358 19.6053300
## [2287] 21.3282581 21.4616139 21.7673517 22.3792081 25.3474192 27.7542633
## [2293] 31.2905447 35.3871840 35.7003598 47.7892125 52.2617451 68.8810473
## [2299] 130.1752467barplot(cah.ward$height)
Perte d’inertie quand on passe de k à k+1 classes. Au début faible perte d’inertie donc le regroupement est pertinent. La dernière hauteur représente la perte d’inertie inter-classe quand on passe de 2 à 1 classe. La perte est importante donc le regroupement est non pertinent.
Combien de groupes garder ? La perte devient plus importante quand on passe de 4 à 3 classes. Donc on peut garder 4 classes. Si on sépare en 5 classes, alors y aura un groupe très petit.
plot(cah.ward, hang =-1,main="ward.D2",cex=0.2)
K=4
rect.hclust(cah.ward,K)
groupes.cah <- cutree(cah.ward, K)
groupes.cah## [1] 1 2 2 2 2 2 2 1 1 2 2 1 1 1 2 2 2 2 2 2 2 2 3 1 1 2 2 2 2 2 2 2 2 2 2 2 2
## [38] 2 1 1 1 2 1 2 1 2 2 2 2 1 2 1 2 3 2 2 1 1 2 2 2 2 2 2 2 2 1 1 1 2 1 1 1 3
## [75] 2 1 1 1 1 1 2 2 1 1 1 2 1 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1 1 1 4 1 4 4 4
## [112] 4 1 1 3 2 1 2 2 4 4 4 4 1 1 2 3 3 3 3 3 3 3 3 3 3 4 3 3 1 4 3 4 4 3 3 3 4
## [149] 4 3 3 4 4 4 2 3 3 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 4 4 3 4 3 4
## [186] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 1 3 3 4 4 4 4 4 4 4
## [223] 4 3 3 4 4 4 4 4 4 3 4 4 4 3 3 3 4 4 4 4 4 4 4 4 4 4 1 4 4 4 3 4 4 4 3 3 3
## [260] 4 4 3 3 4 4 4 4 4 4 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4
## [297] 1 1 1 1 3 3 3 4 4 1 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 1 1 3 4 4 4 4 4 4 1 1 3
## [334] 1 1 3 1 1 1 1 1 1 1 3 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [371] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 3 3 2 2
## [408] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 1 1 2 2 1 1 1 1 2 3 2 2 2 3 3
## [445] 2 2 2 2 2 2 2 1 3 2 1 3 3 3 3 3 3 3 3 3 3 3 1 4 4 4 4 4 4 4 4 3 2 3 3 4 4
## [482] 4 3 3 3 3 1 4 3 4 4 3 3 3 4 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [519] 3 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3
## [556] 3 3 4 4 4 4 4 4 4 4 4 4 4 3 4 4 3 3 4 4 4 4 4 4 4 4 4 3 4 3 4 4 4 4 4 4 4
## [593] 4 4 4 4 4 4 4 4 4 4 3 4 3 3 3 3 4 4 4 4 4 4 3 3 3 4 4 4 1 3 4 4 4 4 4 4 4
## [630] 4 4 3 1 3 3 3 3 3 3 3 4 4 4 4 4 4 4 3 4 4 4 4 1 1 1 4 1 1 2 1 3 1 1 2 1 1
## [667] 2 2 2 2 3 3 1 1 3 3 2 2 2 2 2 1 1 1 1 1 2 2 1 1 3 3 3 2 2 3 2 2 3 1 1 2 3
## [704] 2 3 1 1 2 2 2 1 1 2 2 2 2 2 2 2 2 1 1 1 2 3 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2
## [741] 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 2 1 2 2 2 1 1 2 2 1 2 2 2 2 1 1 3 2 2 2 2 3
## [778] 1 2 2 2 2 1 1 1 3 2 2 2 2 2 3 2 2 3 1 1 3 2 1 4 1 4 1 1 1 1 1 1 1 1 1 1 3
## [815] 1 1 1 3 4 4 4 4 1 1 3 3 1 4 1 4 3 3 4 3 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4
## [852] 4 3 3 3 3 4 4 4 4 3 3 3 4 4 4 1 4 4 4 4 4 3 4 4 4 4 3 3 3 3 4 4 4 4 4 4 4
## [889] 4 4 4 4 3 3 4 4 4 4 3 3 3 3 3 3 4 4 4 3 4 3 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4
## [926] 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
## [963] 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 1 3 3 3 4 3 4 4 4 4 4 4 4 4 4 3 3 3 3 4 4 3
## [1000] 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 4 1 1 1 3 3 3 3 3 3 3 4 4 4 1 1 1 1 2 2 2
## [1037] 1 1 2 1 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 1 2
## [1074] 2 3 2 2 2 2 2 2 1 1 1 1 2 1 1 1 1 3 3 2 2 1 2 2 2 1 4 1 1 1 1 3 1 1 3 2 2
## [1111] 1 3 2 2 2 1 1 1 1 1 1 4 1 1 1 1 3 1 3 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 4 3 3
## [1148] 3 3 3 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 3 3 4 4
## [1185] 4 4 3 3 3 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 3 3 3 3 4 4
## [1222] 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3
## [1259] 3 3 4 4 3 4 4 3 3 4 3 4 3 4 3 1 3 3 4 4 4 4 3 3 3 3 3 4 4 3 4 4 3 4 4 4 4
## [1296] 4 4 4 4 4 4 2 3 4 4 4 4 3 1 4 4 4 3 3 3 3 4 4 4 4 4 4 1 3 3 3 3 3 3 3 3 3
## [1333] 2 2 3 1 1 2 3 2 1 2 3 2 1 1 1 1 1 1 3 1 3 2 1 1 1 1 1 1 1 1 1 3 2 2 2 1 1
## [1370] 2 2 2 2 2 2 2 2 1 1 1 1 2 1 1 1 1 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 2 2 3 3 2
## [1407] 2 1 3 1 2 1 1 3 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1 1 1 1 1 1 2 1 1 2 1 3 2 3
## [1444] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 3 2 1 1 2 3 3 3 2 3 2 1 1 1
## [1481] 4 4 1 1 4 1 3 4 4 4 4 3 3 1 1 1 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 1 4 4
## [1518] 4 3 4 4 4 4 4 3 3 3 3 3 3 4 4 4 4 3 3 3 4 4 4 4 4 4 3 2 1 4 4 4 3 4 4 4 4
## [1555] 4 4 3 3 3 4 3 4 4 3 4 4 4 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4
## [1592] 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 3 3 3 4 4 3 4 3 3 3 3 4 4 4 4 3 4 4 4 4 4
## [1629] 4 3 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 1 3 3 4 4 4 4 4
## [1666] 4 4 4 4 1 3 1 4 4 2 1 4 4 4 4 4 4 4 4 3 3 4 4 1 3 1 4 4 1 4 4 1 1 1 3 4 4
## [1703] 4 1 4 1 1 1 1 1 1 1 2 2 2 3 2 3 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [1740] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2
## [1777] 2 1 1 2 3 3 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1
## [1814] 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 1 4 4 4 4 4 4 1 1 1 1 1 2 2
## [1851] 1 4 4 4 4 1 1 2 2 3 2 1 3 1 1 1 3 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 1 3 3 4
## [1888] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4
## [1925] 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4
## [1962] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4
## [1999] 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 1 3 4 4
## [2036] 4 4 4 4 4 4 1 1 4 1 4 1 3 2 3 4 4 4 1 1 1 2 1 2 3 2 2 2 1 1 1 1 1 1 2 1 1
## [2073] 1 1 2 3 2 3 3 1 1 1 1 1 1 1 1 1 1 2 2 2 3 3 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2
## [2110] 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3
## [2147] 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 2 2 2 2 2 2 2 2 2 2
## [2184] 2 2 2 1 1 2 1 1 1 2 3 2 2 2 2 3 1 1 2 1 1 3 2 2 1 1 1 1 2 1 1 2 2 2 2 2 2
## [2221] 3 3 3 1 1 1 1 1 1 1 3 1 4 4 3 3 3 3 3 1 1 4 4 4 4 4 4 3 2 3 3 4 1 4 4 4 4
## [2258] 4 4 4 4 4 3 2 3 3 3 4 4 3 3 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 4 4 4 3 4 3
## [2295] 3 3 3 1 3 4table(groupes.cah)## groupes.cah
## 1 2 3 4
## 387 568 423 922Interprétation des groupes
for (i in 1:K)
{ cat("groupe", i,"\n")
I=which(groupes.cah==i)
print(rownames(data)[I]) }## groupe 1
## [1] "1" "8" "9" "12" "13" "14" "24" "25" "39" "40"
## [11] "41" "43" "45" "50" "52" "57" "58" "67" "68" "69"
## [21] "71" "72" "73" "76" "77" "78" "79" "80" "83" "84"
## [31] "85" "87" "88" "89" "90" "95" "96" "97" "98" "103"
## [41] "104" "105" "106" "108" "113" "114" "117" "124" "125" "140"
## [51] "213" "249" "297" "298" "299" "300" "306" "322" "323" "331"
## [61] "332" "334" "335" "337" "338" "339" "340" "341" "342" "343"
## [71] "397" "422" "430" "431" "434" "435" "436" "437" "452" "455"
## [81] "467" "487" "621" "633" "653" "654" "655" "657" "658" "660"
## [91] "662" "663" "665" "666" "673" "674" "682" "683" "684" "685"
## [101] "686" "689" "690" "700" "701" "706" "707" "711" "712" "721"
## [111] "722" "723" "753" "754" "755" "757" "761" "762" "765" "770"
## [121] "771" "778" "783" "784" "785" "796" "797" "800" "802" "804"
## [131] "805" "806" "807" "808" "809" "810" "811" "812" "813" "815"
## [141] "816" "817" "823" "824" "827" "829" "867" "978" "1017" "1018"
## [151] "1019" "1030" "1031" "1032" "1033" "1037" "1038" "1040" "1049" "1050"
## [161] "1065" "1066" "1072" "1082" "1083" "1084" "1085" "1087" "1088" "1089"
## [171] "1090" "1095" "1099" "1101" "1102" "1103" "1104" "1106" "1107" "1111"
## [181] "1116" "1117" "1118" "1119" "1120" "1121" "1123" "1124" "1125" "1126"
## [191] "1128" "1274" "1309" "1323" "1336" "1337" "1341" "1345" "1346" "1347"
## [201] "1348" "1349" "1350" "1352" "1355" "1356" "1357" "1358" "1359" "1360"
## [211] "1361" "1362" "1363" "1368" "1369" "1378" "1379" "1380" "1381" "1383"
## [221] "1384" "1385" "1386" "1396" "1397" "1398" "1399" "1400" "1401" "1408"
## [231] "1410" "1412" "1413" "1425" "1430" "1431" "1432" "1433" "1434" "1435"
## [241] "1437" "1438" "1440" "1444" "1445" "1446" "1447" "1448" "1449" "1450"
## [251] "1451" "1452" "1453" "1454" "1455" "1456" "1457" "1458" "1462" "1463"
## [261] "1464" "1465" "1466" "1469" "1470" "1478" "1479" "1480" "1483" "1484"
## [271] "1486" "1494" "1495" "1496" "1497" "1515" "1546" "1658" "1670" "1672"
## [281] "1676" "1689" "1691" "1694" "1697" "1698" "1699" "1704" "1706" "1707"
## [291] "1708" "1709" "1710" "1711" "1712" "1771" "1772" "1778" "1779" "1784"
## [301] "1811" "1812" "1813" "1815" "1816" "1817" "1818" "1819" "1820" "1821"
## [311] "1822" "1823" "1824" "1825" "1826" "1837" "1844" "1845" "1846" "1847"
## [321] "1848" "1851" "1856" "1857" "1862" "1864" "1865" "1866" "1884" "2032"
## [331] "2042" "2043" "2045" "2047" "2054" "2055" "2056" "2058" "2064" "2065"
## [341] "2066" "2067" "2068" "2069" "2071" "2072" "2073" "2074" "2080" "2081"
## [351] "2082" "2083" "2084" "2085" "2086" "2087" "2088" "2089" "2112" "2156"
## [361] "2187" "2188" "2190" "2191" "2192" "2200" "2201" "2203" "2204" "2208"
## [371] "2209" "2210" "2211" "2213" "2214" "2224" "2225" "2226" "2227" "2228"
## [381] "2229" "2230" "2232" "2240" "2241" "2253" "2298"
## groupe 2
## [1] "2" "3" "4" "5" "6" "7" "10" "11" "15" "16"
## [11] "17" "18" "19" "20" "21" "22" "26" "27" "28" "29"
## [21] "30" "31" "32" "33" "34" "35" "36" "37" "38" "42"
## [31] "44" "46" "47" "48" "49" "51" "53" "55" "56" "59"
## [41] "60" "61" "62" "63" "64" "65" "66" "70" "75" "81"
## [51] "82" "86" "91" "92" "93" "94" "99" "100" "101" "102"
## [61] "116" "118" "119" "126" "155" "345" "346" "347" "348" "350"
## [71] "351" "352" "353" "354" "355" "356" "357" "358" "359" "360"
## [81] "361" "362" "363" "364" "365" "366" "367" "368" "369" "370"
## [91] "371" "372" "373" "374" "375" "376" "377" "378" "379" "380"
## [101] "381" "382" "383" "384" "385" "387" "388" "389" "390" "391"
## [111] "392" "393" "394" "395" "396" "398" "399" "400" "401" "402"
## [121] "403" "406" "407" "408" "409" "410" "411" "412" "413" "414"
## [131] "415" "416" "417" "418" "419" "420" "421" "423" "424" "425"
## [141] "426" "427" "428" "429" "432" "433" "438" "440" "441" "442"
## [151] "445" "446" "447" "448" "449" "450" "451" "454" "477" "659"
## [161] "664" "667" "668" "669" "670" "677" "678" "679" "680" "681"
## [171] "687" "688" "694" "695" "697" "698" "702" "704" "708" "709"
## [181] "710" "713" "714" "715" "716" "717" "718" "719" "720" "724"
## [191] "726" "727" "728" "729" "730" "731" "732" "733" "734" "736"
## [201] "737" "738" "739" "740" "741" "742" "743" "744" "745" "746"
## [211] "747" "748" "749" "750" "751" "752" "756" "758" "759" "760"
## [221] "763" "764" "766" "767" "768" "769" "773" "774" "775" "776"
## [231] "779" "780" "781" "782" "787" "788" "789" "790" "791" "793"
## [241] "794" "799" "1034" "1035" "1036" "1039" "1041" "1042" "1043" "1044"
## [251] "1045" "1046" "1047" "1048" "1051" "1052" "1053" "1054" "1055" "1056"
## [261] "1057" "1058" "1059" "1060" "1061" "1062" "1063" "1064" "1067" "1068"
## [271] "1069" "1070" "1071" "1073" "1074" "1076" "1077" "1078" "1079" "1080"
## [281] "1081" "1086" "1093" "1094" "1096" "1097" "1098" "1109" "1110" "1113"
## [291] "1114" "1115" "1302" "1333" "1334" "1338" "1340" "1342" "1344" "1354"
## [301] "1365" "1366" "1367" "1370" "1371" "1372" "1373" "1374" "1375" "1376"
## [311] "1377" "1382" "1387" "1388" "1389" "1390" "1391" "1392" "1393" "1394"
## [321] "1395" "1402" "1403" "1406" "1407" "1411" "1415" "1416" "1417" "1418"
## [331] "1419" "1420" "1421" "1422" "1423" "1424" "1426" "1427" "1428" "1429"
## [341] "1436" "1439" "1442" "1459" "1460" "1461" "1468" "1471" "1475" "1477"
## [351] "1545" "1675" "1713" "1714" "1715" "1717" "1719" "1720" "1721" "1722"
## [361] "1723" "1725" "1726" "1727" "1728" "1729" "1730" "1731" "1732" "1733"
## [371] "1734" "1735" "1736" "1737" "1738" "1739" "1740" "1741" "1742" "1743"
## [381] "1744" "1745" "1746" "1747" "1748" "1749" "1750" "1751" "1752" "1753"
## [391] "1754" "1756" "1757" "1758" "1759" "1760" "1761" "1762" "1763" "1764"
## [401] "1765" "1766" "1767" "1768" "1769" "1770" "1773" "1774" "1775" "1776"
## [411] "1777" "1780" "1783" "1785" "1786" "1787" "1788" "1789" "1790" "1791"
## [421] "1792" "1793" "1794" "1795" "1796" "1797" "1798" "1799" "1800" "1801"
## [431] "1802" "1803" "1804" "1805" "1806" "1807" "1808" "1809" "1810" "1814"
## [441] "1827" "1828" "1829" "1830" "1831" "1832" "1833" "1834" "1849" "1850"
## [451] "1858" "1859" "1861" "2049" "2057" "2059" "2061" "2062" "2063" "2070"
## [461] "2075" "2077" "2090" "2091" "2092" "2095" "2096" "2097" "2098" "2099"
## [471] "2100" "2101" "2102" "2103" "2105" "2106" "2107" "2108" "2109" "2110"
## [481] "2111" "2113" "2114" "2115" "2116" "2117" "2118" "2119" "2120" "2121"
## [491] "2122" "2123" "2124" "2125" "2126" "2127" "2129" "2130" "2131" "2132"
## [501] "2133" "2134" "2135" "2136" "2137" "2138" "2139" "2140" "2141" "2142"
## [511] "2143" "2144" "2145" "2147" "2148" "2149" "2150" "2151" "2152" "2153"
## [521] "2154" "2155" "2157" "2158" "2159" "2160" "2161" "2162" "2163" "2164"
## [531] "2165" "2166" "2167" "2168" "2169" "2170" "2171" "2174" "2175" "2176"
## [541] "2177" "2178" "2179" "2180" "2181" "2182" "2183" "2184" "2185" "2186"
## [551] "2189" "2193" "2195" "2196" "2197" "2198" "2202" "2206" "2207" "2212"
## [561] "2215" "2216" "2217" "2218" "2219" "2220" "2249" "2264"
## groupe 3
## [1] "23" "54" "74" "115" "127" "128" "129" "130" "131" "132"
## [11] "133" "134" "135" "136" "138" "139" "142" "145" "146" "147"
## [21] "150" "151" "156" "157" "168" "169" "182" "184" "201" "202"
## [31] "214" "215" "224" "225" "232" "236" "237" "238" "253" "257"
## [41] "258" "259" "262" "263" "270" "271" "272" "288" "289" "301"
## [51] "302" "303" "307" "320" "321" "324" "333" "336" "344" "349"
## [61] "386" "404" "405" "439" "443" "444" "453" "456" "457" "458"
## [71] "459" "460" "461" "462" "463" "464" "465" "466" "476" "478"
## [81] "479" "483" "484" "485" "486" "489" "492" "493" "494" "496"
## [91] "497" "498" "499" "500" "501" "502" "519" "520" "533" "534"
## [101] "535" "536" "537" "553" "554" "555" "556" "557" "569" "572"
## [111] "573" "583" "585" "603" "605" "606" "607" "608" "615" "616"
## [121] "617" "622" "632" "634" "635" "636" "637" "638" "639" "640"
## [131] "648" "661" "671" "672" "675" "676" "691" "692" "693" "696"
## [141] "699" "703" "705" "725" "735" "772" "777" "786" "792" "795"
## [151] "798" "814" "818" "825" "826" "831" "832" "834" "845" "846"
## [161] "853" "854" "855" "856" "861" "862" "863" "873" "878" "879"
## [171] "880" "881" "893" "894" "899" "900" "901" "902" "903" "904"
## [181] "908" "910" "921" "922" "937" "938" "943" "963" "964" "965"
## [191] "966" "967" "979" "980" "981" "983" "993" "994" "995" "996"
## [201] "999" "1004" "1005" "1020" "1021" "1022" "1023" "1024" "1025" "1026"
## [211] "1075" "1091" "1092" "1105" "1108" "1112" "1127" "1129" "1137" "1138"
## [221] "1139" "1140" "1141" "1142" "1143" "1144" "1146" "1147" "1148" "1149"
## [231] "1150" "1158" "1159" "1170" "1171" "1172" "1173" "1174" "1181" "1182"
## [241] "1187" "1188" "1189" "1192" "1209" "1216" "1217" "1218" "1219" "1225"
## [251] "1226" "1258" "1259" "1260" "1263" "1266" "1267" "1269" "1271" "1273"
## [261] "1275" "1276" "1281" "1282" "1283" "1284" "1285" "1288" "1291" "1303"
## [271] "1308" "1313" "1314" "1315" "1316" "1324" "1325" "1326" "1327" "1328"
## [281] "1329" "1330" "1331" "1332" "1335" "1339" "1343" "1351" "1353" "1364"
## [291] "1404" "1405" "1409" "1414" "1441" "1443" "1467" "1472" "1473" "1474"
## [301] "1476" "1487" "1492" "1493" "1514" "1519" "1525" "1526" "1527" "1528"
## [311] "1529" "1530" "1535" "1536" "1537" "1544" "1550" "1557" "1558" "1559"
## [321] "1561" "1564" "1568" "1569" "1570" "1583" "1600" "1601" "1608" "1609"
## [331] "1610" "1613" "1615" "1616" "1617" "1618" "1623" "1630" "1639" "1640"
## [341] "1651" "1652" "1659" "1660" "1671" "1685" "1686" "1690" "1700" "1716"
## [351] "1718" "1724" "1755" "1781" "1782" "1835" "1836" "1860" "1863" "1867"
## [361] "1875" "1876" "1885" "1886" "1904" "1917" "1918" "1928" "1940" "1950"
## [371] "1951" "1979" "1994" "1999" "2000" "2027" "2028" "2033" "2048" "2050"
## [381] "2060" "2076" "2078" "2079" "2093" "2094" "2104" "2128" "2146" "2172"
## [391] "2173" "2194" "2199" "2205" "2221" "2222" "2223" "2231" "2235" "2236"
## [401] "2237" "2238" "2239" "2248" "2250" "2251" "2263" "2265" "2266" "2267"
## [411] "2270" "2271" "2278" "2279" "2280" "2281" "2282" "2292" "2294" "2295"
## [421] "2296" "2297" "2299"
## groupe 4
## [1] "107" "109" "110" "111" "112" "120" "121" "122" "123" "137"
## [11] "141" "143" "144" "148" "149" "152" "153" "154" "158" "159"
## [21] "160" "161" "162" "163" "164" "165" "166" "167" "170" "171"
## [31] "172" "173" "174" "175" "176" "177" "178" "179" "180" "181"
## [41] "183" "185" "186" "187" "188" "189" "190" "191" "192" "193"
## [51] "194" "195" "196" "197" "198" "199" "200" "203" "204" "205"
## [61] "206" "207" "208" "209" "210" "211" "212" "216" "217" "218"
## [71] "219" "220" "221" "222" "223" "226" "227" "228" "229" "230"
## [81] "231" "233" "234" "235" "239" "240" "241" "242" "243" "244"
## [91] "245" "246" "247" "248" "250" "251" "252" "254" "255" "256"
## [101] "260" "261" "264" "265" "266" "267" "268" "269" "273" "274"
## [111] "275" "276" "277" "278" "279" "280" "281" "282" "283" "284"
## [121] "285" "286" "287" "290" "291" "292" "293" "294" "295" "296"
## [131] "304" "305" "308" "309" "310" "311" "312" "313" "314" "315"
## [141] "316" "317" "318" "319" "325" "326" "327" "328" "329" "330"
## [151] "468" "469" "470" "471" "472" "473" "474" "475" "480" "481"
## [161] "482" "488" "490" "491" "495" "503" "504" "505" "506" "507"
## [171] "508" "509" "510" "511" "512" "513" "514" "515" "516" "517"
## [181] "518" "521" "522" "523" "524" "525" "526" "527" "528" "529"
## [191] "530" "531" "532" "538" "539" "540" "541" "542" "543" "544"
## [201] "545" "546" "547" "548" "549" "550" "551" "552" "558" "559"
## [211] "560" "561" "562" "563" "564" "565" "566" "567" "568" "570"
## [221] "571" "574" "575" "576" "577" "578" "579" "580" "581" "582"
## [231] "584" "586" "587" "588" "589" "590" "591" "592" "593" "594"
## [241] "595" "596" "597" "598" "599" "600" "601" "602" "604" "609"
## [251] "610" "611" "612" "613" "614" "618" "619" "620" "623" "624"
## [261] "625" "626" "627" "628" "629" "630" "631" "641" "642" "643"
## [271] "644" "645" "646" "647" "649" "650" "651" "652" "656" "801"
## [281] "803" "819" "820" "821" "822" "828" "830" "833" "835" "836"
## [291] "837" "838" "839" "840" "841" "842" "843" "844" "847" "848"
## [301] "849" "850" "851" "852" "857" "858" "859" "860" "864" "865"
## [311] "866" "868" "869" "870" "871" "872" "874" "875" "876" "877"
## [321] "882" "883" "884" "885" "886" "887" "888" "889" "890" "891"
## [331] "892" "895" "896" "897" "898" "905" "906" "907" "909" "911"
## [341] "912" "913" "914" "915" "916" "917" "918" "919" "920" "923"
## [351] "924" "925" "926" "927" "928" "929" "930" "931" "932" "933"
## [361] "934" "935" "936" "939" "940" "941" "942" "944" "945" "946"
## [371] "947" "948" "949" "950" "951" "952" "953" "954" "955" "956"
## [381] "957" "958" "959" "960" "961" "962" "968" "969" "970" "971"
## [391] "972" "973" "974" "975" "976" "977" "982" "984" "985" "986"
## [401] "987" "988" "989" "990" "991" "992" "997" "998" "1000" "1001"
## [411] "1002" "1003" "1006" "1007" "1008" "1009" "1010" "1011" "1012" "1013"
## [421] "1014" "1015" "1016" "1027" "1028" "1029" "1100" "1122" "1130" "1131"
## [431] "1132" "1133" "1134" "1135" "1136" "1145" "1151" "1152" "1153" "1154"
## [441] "1155" "1156" "1157" "1160" "1161" "1162" "1163" "1164" "1165" "1166"
## [451] "1167" "1168" "1169" "1175" "1176" "1177" "1178" "1179" "1180" "1183"
## [461] "1184" "1185" "1186" "1190" "1191" "1193" "1194" "1195" "1196" "1197"
## [471] "1198" "1199" "1200" "1201" "1202" "1203" "1204" "1205" "1206" "1207"
## [481] "1208" "1210" "1211" "1212" "1213" "1214" "1215" "1220" "1221" "1222"
## [491] "1223" "1224" "1227" "1228" "1229" "1230" "1231" "1232" "1233" "1234"
## [501] "1235" "1236" "1237" "1238" "1239" "1240" "1241" "1242" "1243" "1244"
## [511] "1245" "1246" "1247" "1248" "1249" "1250" "1251" "1252" "1253" "1254"
## [521] "1255" "1256" "1257" "1261" "1262" "1264" "1265" "1268" "1270" "1272"
## [531] "1277" "1278" "1279" "1280" "1286" "1287" "1289" "1290" "1292" "1293"
## [541] "1294" "1295" "1296" "1297" "1298" "1299" "1300" "1301" "1304" "1305"
## [551] "1306" "1307" "1310" "1311" "1312" "1317" "1318" "1319" "1320" "1321"
## [561] "1322" "1481" "1482" "1485" "1488" "1489" "1490" "1491" "1498" "1499"
## [571] "1500" "1501" "1502" "1503" "1504" "1505" "1506" "1507" "1508" "1509"
## [581] "1510" "1511" "1512" "1513" "1516" "1517" "1518" "1520" "1521" "1522"
## [591] "1523" "1524" "1531" "1532" "1533" "1534" "1538" "1539" "1540" "1541"
## [601] "1542" "1543" "1547" "1548" "1549" "1551" "1552" "1553" "1554" "1555"
## [611] "1556" "1560" "1562" "1563" "1565" "1566" "1567" "1571" "1572" "1573"
## [621] "1574" "1575" "1576" "1577" "1578" "1579" "1580" "1581" "1582" "1584"
## [631] "1585" "1586" "1587" "1588" "1589" "1590" "1591" "1592" "1593" "1594"
## [641] "1595" "1596" "1597" "1598" "1599" "1602" "1603" "1604" "1605" "1606"
## [651] "1607" "1611" "1612" "1614" "1619" "1620" "1621" "1622" "1624" "1625"
## [661] "1626" "1627" "1628" "1629" "1631" "1632" "1633" "1634" "1635" "1636"
## [671] "1637" "1638" "1641" "1642" "1643" "1644" "1645" "1646" "1647" "1648"
## [681] "1649" "1650" "1653" "1654" "1655" "1656" "1657" "1661" "1662" "1663"
## [691] "1664" "1665" "1666" "1667" "1668" "1669" "1673" "1674" "1677" "1678"
## [701] "1679" "1680" "1681" "1682" "1683" "1684" "1687" "1688" "1692" "1693"
## [711] "1695" "1696" "1701" "1702" "1703" "1705" "1838" "1839" "1840" "1841"
## [721] "1842" "1843" "1852" "1853" "1854" "1855" "1868" "1869" "1870" "1871"
## [731] "1872" "1873" "1874" "1877" "1878" "1879" "1880" "1881" "1882" "1883"
## [741] "1887" "1888" "1889" "1890" "1891" "1892" "1893" "1894" "1895" "1896"
## [751] "1897" "1898" "1899" "1900" "1901" "1902" "1903" "1905" "1906" "1907"
## [761] "1908" "1909" "1910" "1911" "1912" "1913" "1914" "1915" "1916" "1919"
## [771] "1920" "1921" "1922" "1923" "1924" "1925" "1926" "1927" "1929" "1930"
## [781] "1931" "1932" "1933" "1934" "1935" "1936" "1937" "1938" "1939" "1941"
## [791] "1942" "1943" "1944" "1945" "1946" "1947" "1948" "1949" "1952" "1953"
## [801] "1954" "1955" "1956" "1957" "1958" "1959" "1960" "1961" "1962" "1963"
## [811] "1964" "1965" "1966" "1967" "1968" "1969" "1970" "1971" "1972" "1973"
## [821] "1974" "1975" "1976" "1977" "1978" "1980" "1981" "1982" "1983" "1984"
## [831] "1985" "1986" "1987" "1988" "1989" "1990" "1991" "1992" "1993" "1995"
## [841] "1996" "1997" "1998" "2001" "2002" "2003" "2004" "2005" "2006" "2007"
## [851] "2008" "2009" "2010" "2011" "2012" "2013" "2014" "2015" "2016" "2017"
## [861] "2018" "2019" "2020" "2021" "2022" "2023" "2024" "2025" "2026" "2029"
## [871] "2030" "2031" "2034" "2035" "2036" "2037" "2038" "2039" "2040" "2041"
## [881] "2044" "2046" "2051" "2052" "2053" "2233" "2234" "2242" "2243" "2244"
## [891] "2245" "2246" "2247" "2252" "2254" "2255" "2256" "2257" "2258" "2259"
## [901] "2260" "2261" "2262" "2268" "2269" "2272" "2273" "2274" "2275" "2276"
## [911] "2277" "2283" "2284" "2285" "2286" "2287" "2288" "2289" "2290" "2291"
## [921] "2293" "2300"Caractéristiques de chaque groupe.
Means_groupes <- matrix(NA, nrow=K, ncol=dim(data)[2])
colnames(Means_groupes)=colnames(data)
rownames(Means_groupes) =1:K
for (i in 1:K)
Means_groupes[i,]<- colMeans(data[groupes.cah==i,])
round(Means_groupes)## MinTemp MaxTemp Rainfall Humidity9am Humidity3pm Pressure9am Pressure3pm
## 1 18 23 1 65 63 1019 1017
## 2 20 25 3 78 74 1014 1013
## 3 17 21 9 81 78 1013 1011
## 4 14 19 2 65 62 1022 1020
## Temp9am Temp3pm AvgTemp
## 1 21 22 21
## 2 23 24 23
## 3 19 20 19
## 4 17 18 17Les groupes sont séparés selon la température: groupe 1 : AvgTemp = 21 groupe 2 : AvgTemp = 23 groupe 3 : AvgTemp = 19 groupe 4 : AvgTemp = 17
Kmeans
Avec K=4 classes d’après la CAH
kmeans.result <- kmeans(data.cr,centers=K)
kmeans.result## K-means clustering with 4 clusters of sizes 612, 438, 415, 835
##
## Cluster means:
## MinTemp MaxTemp Rainfall Humidity9am Humidity3pm Pressure9am
## 1 0.4660997 0.6837587 -0.26133620 -0.4169394 -0.4055712 0.1295143
## 2 1.3350061 1.2353981 0.01248747 0.8413376 0.8374997 -0.8277244
## 3 -0.1612103 -0.4072096 0.73852561 0.8788391 0.8247842 -0.8010838
## 4 -0.9617766 -0.9467937 -0.18205974 -0.5725236 -0.5519769 0.7374016
## Pressure3pm Temp9am Temp3pm AvgTemp
## 1 0.1657267 0.6658335 0.6774093 0.5921291
## 2 -0.7870284 1.2224378 1.2079724 1.3275937
## 3 -0.8710366 -0.3836626 -0.4199530 -0.2917815
## 4 0.7242801 -0.9385603 -0.9214202 -0.9853649
##
## Clustering vector:
## [1] 1 1 2 2 2 1 1 1 1 1 2 1 1 1 1 1 1 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 2 2 2 2 1
## [38] 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 2 2 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1
## [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 1 1 3 1 2 2 1 1 1 1 1 1 1 1 1
## [112] 1 1 1 2 1 1 1 1 1 1 4 4 1 1 3 3 3 3 3 3 3 3 3 3 3 1 3 3 1 4 3 3 4 3 3 3 4
## [149] 4 3 3 1 4 4 3 3 3 4 4 3 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 3 4 4 4 4 4 3 4
## [186] 4 4 3 4 4 4 4 4 4 4 3 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 1 3 3 4 4 3 4 4 4 4
## [223] 4 3 3 4 4 3 4 4 4 3 4 4 4 3 3 3 4 4 4 4 4 4 4 4 4 1 1 3 4 4 3 3 4 4 3 3 3
## [260] 4 4 4 3 4 4 4 4 4 3 3 3 2 4 4 4 4 4 4 4 1 1 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4
## [297] 1 1 1 1 3 3 3 4 4 1 3 4 4 4 4 4 4 4 4 4 4 4 3 3 3 1 1 3 4 4 4 4 4 3 1 1 3
## [334] 1 1 3 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2
## [371] 2 2 2 2 1 2 1 2 2 2 2 2 2 1 2 3 2 2 1 2 2 2 2 1 2 1 1 2 2 1 1 2 2 2 2 2 2
## [408] 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 2 2 2 2 2 3 1 1 1 1 1 1 1 1 1 2 2 2 2 3 3
## [445] 2 2 2 2 2 2 1 1 3 2 1 3 3 3 3 3 1 3 3 1 1 3 1 4 4 4 4 4 4 4 1 3 3 3 3 4 4
## [482] 4 3 3 3 3 1 4 4 3 4 3 3 3 4 3 3 3 3 3 3 3 3 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4
## [519] 3 3 4 4 4 3 4 4 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3
## [556] 3 3 4 4 4 4 4 4 4 3 4 4 4 3 3 4 4 3 4 4 4 4 4 4 4 4 4 3 4 3 3 3 4 4 4 4 4
## [593] 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 4 4 4 3 3 3 3 4 4 4 1 3 4 4 4 4 4 4 4
## [630] 4 4 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 1 3 4 4 4 4 1 1 1 4 1 1 1 1 1 1 1 1 1 1
## [667] 1 2 2 2 3 3 1 1 2 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 3 3 3 2 2 2 2 2 3 1 1 2 2
## [704] 1 1 1 1 2 2 1 1 1 3 2 2 2 2 2 2 2 1 1 1 2 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 1
## [741] 1 1 2 1 2 2 2 2 2 2 2 2 1 1 1 1 1 1 2 2 1 1 1 1 1 2 2 2 1 1 1 2 2 2 2 2 3
## [778] 1 2 2 2 1 1 1 1 3 2 2 2 2 2 2 2 3 2 1 1 2 2 1 4 1 4 1 1 1 1 1 1 1 1 1 1 2
## [815] 1 1 1 3 3 4 4 4 1 3 3 3 1 4 1 1 4 3 4 3 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4
## [852] 4 3 3 3 3 4 4 4 4 3 3 3 4 4 4 3 4 4 4 4 4 4 4 4 4 4 3 3 3 3 4 4 4 4 4 4 4
## [889] 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 4 4 3 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4
## [926] 4 4 4 3 4 4 4 4 4 4 4 3 3 4 4 4 4 3 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4
## [963] 3 3 3 3 3 4 3 4 4 4 4 4 4 4 4 4 3 3 3 4 3 3 4 4 4 4 4 4 4 4 3 3 3 3 4 4 3
## [1000] 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 4 1 1 1 1 3 3 3 3 3 3 4 1 1 1 1 1 1 2 2 1
## [1037] 1 1 2 1 1 2 2 1 1 2 1 1 1 1 2 1 2 2 2 2 2 2 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1
## [1074] 1 2 2 2 2 2 2 2 1 1 1 1 2 1 1 1 1 1 2 2 1 1 2 2 1 1 1 1 1 1 1 3 1 1 3 3 2
## [1111] 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1 3 1 3 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3
## [1148] 3 3 3 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 3 3 4 4
## [1185] 4 4 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 3 3 3 3 4 4
## [1222] 4 4 3 3 3 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3
## [1259] 3 3 4 4 3 4 4 3 3 3 4 3 3 4 3 3 3 3 4 4 4 4 1 3 3 3 3 4 4 3 4 4 3 4 4 4 4
## [1296] 4 4 4 4 4 1 1 3 3 4 4 4 3 1 4 4 4 4 4 4 1 4 4 4 1 1 1 1 3 2 2 3 3 3 3 3 3
## [1333] 2 2 2 3 1 1 2 3 1 2 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1
## [1370] 1 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 2 3 2 2 2 2 2 2 1 1 1 1 1 1 1 2 3 3 2
## [1407] 2 1 1 1 2 1 1 1 2 2 2 2 2 2 2 2 2 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 3 2 1
## [1444] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 1 2 2 2 2 2 2 1 1 1 1
## [1481] 1 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 1 4 4
## [1518] 3 3 4 4 4 4 4 3 3 3 3 3 3 3 3 3 4 3 3 3 4 4 4 4 4 4 3 3 4 4 4 4 3 4 4 4 4
## [1555] 4 4 3 3 3 4 3 4 3 4 4 4 4 3 3 3 4 4 4 4 4 4 4 4 4 4 4 3 3 3 4 4 4 4 4 4 4
## [1592] 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 3 3 3 3 3 3 3 4 3 3 3 3 4 4 4 4 3 3 4 4 4 4
## [1629] 4 3 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 1 3 3 4 4 4 4 4
## [1666] 4 4 4 4 1 1 1 4 1 1 1 3 4 4 4 1 4 4 4 1 4 4 4 1 2 1 1 4 1 1 1 1 1 1 1 1 1
## [1703] 1 1 1 1 1 1 1 1 1 1 2 2 2 3 3 3 2 1 2 2 3 3 2 2 2 2 2 1 2 2 2 2 1 2 1 1 2
## [1740] 1 2 2 1 1 1 1 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1
## [1777] 1 1 1 2 2 2 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 1 1 1 1 1
## [1814] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 2 2 2 3 3 1 1 1 1 1 1 1 1 1 1 1 1 2 2
## [1851] 1 1 1 4 1 1 1 2 2 2 2 1 4 1 1 1 3 4 4 4 4 4 4 4 1 3 4 4 4 4 4 4 4 1 3 1 4
## [1888] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4
## [1925] 4 4 4 3 3 4 3 3 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4
## [1962] 4 4 4 4 4 4 4 4 4 4 4 4 4 1 3 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 3
## [1999] 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4
## [2036] 4 4 3 4 4 4 1 1 3 4 4 1 2 2 3 4 4 4 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1
## [2073] 1 1 1 2 2 3 1 1 1 1 1 1 1 1 1 1 1 1 2 2 3 3 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1
## [2110] 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2147] 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 1 2 2 1 2 2 2 2 2 2 2 3 2 2 1 1 1 1 2 2 2 2
## [2184] 2 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 1 1 2 1 1 1 2 2 1 1 1 1 1 1 1 2 2 2 3 3 2
## [2221] 2 2 3 1 1 1 1 1 1 1 1 1 3 1 3 1 3 1 3 1 1 4 4 4 4 4 4 3 3 3 3 3 1 4 4 4 4
## [2258] 4 4 4 4 4 3 3 3 3 3 4 4 3 3 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 4 4 4 3 4 3
## [2295] 3 3 3 3 4 3
##
## Within cluster sum of squares by cluster:
## [1] 1755.488 1789.869 3423.281 2972.634
## (between_SS / total_SS = 56.8 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"kmeans.result <- kmeans(data.cr,centers=K)
kmeans.result$size## [1] 468 760 641 431Les résultats changent car sont dépendants de l’initialisation —> choisir une bonne initialisation (avec CAH par exemple) ou stabiliser le problème du choix de l’initialisation en lançant plusieurs kmeans.
Initialisation avec CAH
init <- matrix(NA, nrow=K, ncol=dim(data)[2])
colnames(init)=colnames(data)
for (i in 1:K) init[i,] <- colMeans(data.cr[groupes.cah==i,])
init## MinTemp MaxTemp Rainfall Humidity9am Humidity3pm Pressure9am
## [1,] 0.395316840 0.5953474 -0.27315886 -0.4880411 -0.4196290 0.2330355
## [2,] 1.220316283 1.2090205 -0.01216608 0.5702286 0.4895641 -0.6750940
## [3,] -0.008041669 -0.2280792 0.56968186 0.8280126 0.8154354 -0.8037610
## [4,] -0.914019132 -0.8900711 -0.13921108 -0.5263203 -0.4995718 0.6868325
## Pressure3pm Temp9am Temp3pm AvgTemp
## [1,] 0.2623958 0.5931137 0.5957677 0.5100666
## [2,] -0.6247817 1.1791527 1.1892963 1.2541762
## [3,] -0.8574065 -0.1918281 -0.2432001 -0.1204129
## [4,] 0.6681256 -0.8873649 -0.8711591 -0.9314894Attention à bien prendre l’init avec colMeans sur les données centrées réduites parce qu’on lance kmeans sur les données centrées réduites (et sinon problème d’échelle : les centres des classes ne sont pas adaptés)
kmeans.initCAH <- kmeans(data.cr, centers= init)Stabilisation en lançant plusieurs initialisations
kmeans.result <- kmeans(data.cr,centers=K,nstart=1000)Comparaison
table(groupes.cah, kmeans.initCAH$cluster)##
## groupes.cah 1 2 3 4
## 1 377 0 6 4
## 2 156 394 18 0
## 3 29 44 331 19
## 4 50 0 60 812table(groupes.cah,kmeans.result$cluster)##
## groupes.cah 1 2 3 4
## 1 0 3 369 15
## 2 354 0 209 5
## 3 77 7 23 316
## 4 0 750 40 132table(kmeans.initCAH$cluster,kmeans.result$cluster)##
## 1 2 3 4
## 1 1 6 585 20
## 2 384 0 54 0
## 3 46 0 2 367
## 4 0 754 0 81On retrouve ici les mêmes groupes avec kmeans initialisé en CAH et kmeans avec plusieurs initialiations (à label switching près sur les groupes).
Sans a-priori sur le choix de K avec la CAH, comment choisir K ?
#Evaluer la proportion d’inertie intra-classe
inertie.intra <- rep(0,times=10)
for (k in 1:10){
kmeans.result <- kmeans(data.cr,centers=k,nstart=100)
inertie.intra[k] <- kmeans.result$tot.withinss/kmeans.result$totss
}## Warning: did not converge in 10 iterations
## Warning: did not converge in 10 iterations# Graphique
plot(1:10,inertie.intra,type="b",xlab="Nb. de groupes",ylab="% inertie intra")
À partir de K = 4 classes, l’ajout d’un groupe supplémentaire ne diminue pas “significativement” la part d’inertie intra.
Interprétation des classes avec une ACP
kmeans.result <- kmeans(data.cr,centers=K,nstart=1000)
pairs(data, col=kmeans.result$cluster )
ACP
res=PCA(data,scale.unit=TRUE, graph=FALSE)res$eig## eigenvalue percentage of variance cumulative percentage of variance
## comp 1 5.537506e+00 5.537506e+01 55.37506
## comp 2 2.132117e+00 2.132117e+01 76.69623
## comp 3 1.040299e+00 1.040299e+01 87.09922
## comp 4 7.680060e-01 7.680060e+00 94.77928
## comp 5 2.985329e-01 2.985329e+00 97.76461
## comp 6 1.438896e-01 1.438896e+00 99.20350
## comp 7 3.718915e-02 3.718915e-01 99.57539
## comp 8 2.658717e-02 2.658717e-01 99.84126
## comp 9 1.587356e-02 1.587356e-01 100.00000
## comp 10 1.578246e-28 1.578246e-27 100.00000plot(res, choix="var")
axe 1 indique l’importance de la température axe 2 indique l’importance de la pression contre d’humidité
#Plot selon la Température moyenne
plot(res, choix="ind", habillage=10)
#Meth 1 : obtenir le graphe à la main :
plot(res$ind$coord[,1], res$ind$coord[,2], col=kmeans.result$cluster, cex=res$ind$cos2, ylim=c(-4,4))
abline(h=0)
abline(v=0)
Meth 2: en rajoutant la classe au data frame, en lancant une ACP avec la classe comme variable qualitative supplémentaire, et en utilisant l’option habillage de plot :
data.Avecclasse = cbind.data.frame(data, classe = factor(kmeans.result$cluster))
head(data.Avecclasse)## MinTemp MaxTemp Rainfall Humidity9am Humidity3pm Pressure9am Pressure3pm
## 1 18.6 24.5 0.0 53 55 1021.5 1019.6
## 2 19.3 25.2 0.0 77 73 1019.2 1017.6
## 3 20.7 26.4 0.0 73 70 1016.9 1015.4
## 4 20.2 26.7 0.0 70 65 1015.4 1015.0
## 5 20.9 24.7 0.0 85 79 1017.8 1017.1
## 6 19.5 24.9 0.8 82 68 1018.7 1017.6
## Temp9am Temp3pm AvgTemp classe
## 1 22.4 23.4 21.55 4
## 2 22.5 23.4 22.25 4
## 3 23.8 24.2 23.55 1
## 4 23.5 25.4 23.45 4
## 5 22.5 23.2 22.80 1
## 6 21.2 23.3 22.20 4dim(data.Avecclasse)## [1] 2300 11res=PCA(data.Avecclasse,scale.unit=TRUE, quali.sup = 11, graph=FALSE)
plot(res, choix="ind", habillage=11, cex=0.7, select= "cos2 0.7")
Classe 1 : Température moyenne élevée Classe 2 : Température moyenne faible Classe 3 : Température moyenne-moyenne, Humidité faible, Pression élevée Classe 4: Température moyenne-moyenne, Humidité forte, Pression faible
Silhouette
sil= silhouette(kmeans.result$cluster,dist(data.cr))
rownames(sil)=rownames(data)
sil## cluster neighbor sil_width
## 1 4 1 0.5071893662
## 2 4 1 0.2500491350
## 3 1 4 -0.0884206575
## 4 4 1 0.1426632988
## 5 1 4 0.0670352799
## 6 4 1 0.2485626869
## 7 4 1 0.3918536023
## 8 4 1 0.4410930790
## 9 4 1 0.4310854814
## 10 4 1 0.4497186587
## 11 1 4 0.1193733387
## 12 4 1 0.4148779534
## 13 4 3 0.4213309813
## 14 4 1 0.4869277547
## 15 4 1 0.3109118416
## 16 4 1 0.3285003172
## 17 4 1 0.3303597737
## 18 4 1 0.1711168818
## 19 1 4 0.2529182936
## 20 1 4 0.2243790138
## 21 1 4 -0.0050342693
## 22 4 1 0.1975060581
## 23 4 1 0.2084571428
## 24 4 1 0.4510030690
## 25 4 1 0.4406232744
## 26 4 1 0.3730579499
## 27 4 1 0.3336146936
## 28 4 1 0.1755701461
## 29 1 4 0.1805966632
## 30 1 4 0.0579608698
## 31 4 1 0.1855736516
## 32 4 1 0.1391913421
## 33 1 4 0.2103546790
## 34 1 4 0.2992491829
## 35 1 4 -0.1080846030
## 36 4 1 0.1217148516
## 37 4 1 0.2800606485
## 38 4 1 0.1858821424
## 39 4 1 0.3450954997
## 40 4 1 0.3661685822
## 41 4 1 0.5071918053
## 42 4 1 0.4428702580
## 43 4 1 0.4181515174
## 44 4 1 0.2715009881
## 45 4 1 0.3566716419
## 46 4 1 0.3923865580
## 47 4 1 0.2762158466
## 48 1 4 0.2288758177
## 49 4 1 0.2350413013
## 50 4 1 0.4495574870
## 51 4 1 0.1788504702
## 52 4 1 0.3681266544
## 53 4 1 0.3508580932
## 54 1 4 0.0717663082
## 55 1 4 0.0290120867
## 56 1 4 -0.0528987909
## 57 4 1 0.3580276793
## 58 4 1 0.3909747812
## 59 4 1 0.1350833735
## 60 1 4 0.2969041896
## 61 1 4 0.0916012648
## 62 4 1 0.2275390006
## 63 4 1 0.3691566001
## 64 4 1 0.3434648909
## 65 4 1 0.2639309167
## 66 4 1 0.4442835441
## 67 4 1 0.4798817926
## 68 4 1 0.4792693642
## 69 4 1 0.4768752639
## 70 4 1 0.2779802672
## 71 4 3 0.4206490805
## 72 4 3 0.4805554188
## 73 4 2 0.3954891395
## 74 4 1 0.2561268378
## 75 4 1 0.5162786213
## 76 4 1 0.5068782082
## 77 4 3 0.4040760908
## 78 4 3 0.3696986936
## 79 4 3 0.3661271121
## 80 4 1 0.4475476797
## 81 4 1 0.4200400824
## 82 4 1 0.3649901839
## 83 4 1 0.4148633543
## 84 4 1 0.4544019340
## 85 4 1 0.4510126752
## 86 4 1 0.4187205694
## 87 4 1 0.3855529225
## 88 4 1 0.4109400532
## 89 4 1 0.3594807905
## 90 4 1 0.4825471030
## 91 4 1 0.4259570568
## 92 4 1 0.2055160328
## 93 4 1 0.2128138476
## 94 1 4 0.1895919245
## 95 4 2 0.4105202147
## 96 4 3 0.4335024279
## 97 4 3 0.2960628147
## 98 4 1 0.4434991040
## 99 1 4 -0.0047277421
## 100 4 1 0.3500544324
## 101 4 1 0.2217347557
## 102 1 4 0.2079932154
## 103 4 1 0.2109600279
## 104 4 1 0.4748982200
## 105 4 3 0.4530580329
## 106 4 3 0.4021263470
## 107 4 3 0.2116003251
## 108 4 3 0.4641861345
## 109 4 3 0.2143633309
## 110 4 3 0.1960488134
## 111 4 3 0.1037744277
## 112 4 3 0.1694086079
## 113 4 3 0.2897758878
## 114 4 3 0.3745484902
## 115 1 2 0.0747296955
## 116 4 1 0.1554913479
## 117 4 2 0.3690323019
## 118 4 1 0.2371154417
## 119 4 1 0.3102993621
## 120 4 2 0.2851043530
## 121 3 4 0.0018158611
## 122 3 4 0.3007524542
## 123 3 4 0.1011120262
## 124 4 3 0.3178866642
## 125 4 2 0.1784938946
## 126 1 2 0.0587813584
## 127 1 4 -0.0092006837
## 128 2 1 0.0679208795
## 129 2 1 0.2194547780
## 130 1 2 0.0778027617
## 131 2 4 0.0379037261
## 132 2 4 -0.0108570664
## 133 2 4 0.0905762106
## 134 2 4 0.2533311343
## 135 2 4 0.2377205513
## 136 2 3 0.2060838128
## 137 4 3 0.0773729296
## 138 2 4 0.2014118703
## 139 2 4 0.1918154011
## 140 4 3 0.1455400967
## 141 2 3 -0.0055782803
## 142 2 4 0.0997359743
## 143 2 3 0.2694733595
## 144 2 3 0.0261862551
## 145 2 3 0.3617968955
## 146 2 1 0.1225232861
## 147 2 4 0.2171464818
## 148 3 2 0.4782537239
## 149 2 3 0.0326974820
## 150 2 1 0.1227013425
## 151 1 4 -0.0098638340
## 152 2 4 -0.0740510100
## 153 2 3 0.0289445673
## 154 2 3 -0.0235062913
## 155 1 2 0.0450021008
## 156 2 1 0.0449314377
## 157 2 4 0.2544270325
## 158 2 3 -0.0775363052
## 159 3 2 0.2316916203
## 160 2 3 0.0887917102
## 161 3 2 0.1863027530
## 162 3 2 0.2203322340
## 163 3 2 0.1774621699
## 164 3 2 0.5375337581
## 165 3 2 0.5171572331
## 166 3 2 0.5109468240
## 167 3 2 0.3468876309
## 168 2 3 0.2849213917
## 169 2 3 0.3403240284
## 170 2 3 -0.0409237737
## 171 3 2 0.0549544459
## 172 2 3 -0.0069719320
## 173 3 2 0.4459318032
## 174 3 2 0.5240842551
## 175 3 2 0.5254192006
## 176 3 2 0.5237539879
## 177 3 2 0.4847067631
## 178 2 3 0.2154917421
## 179 3 2 0.3843049942
## 180 3 2 0.5306029535
## 181 3 2 0.5044460040
## 182 2 3 -0.0254779525
## 183 3 2 0.4307688622
## 184 2 3 0.2105154223
## 185 2 3 -0.0404372318
## 186 3 2 0.2285350600
## 187 3 2 0.4257133162
## 188 2 3 0.0464504680
## 189 3 2 0.4969380810
## 190 3 2 0.3904924565
## 191 3 2 0.4837509050
## 192 3 2 0.3441001218
## 193 3 2 0.5093054750
## 194 3 2 0.4986917500
## 195 3 2 0.2909649929
## 196 2 3 0.0810907964
## 197 3 2 0.2156257315
## 198 3 2 0.5311811533
## 199 3 2 0.2788079918
## 200 3 2 0.1225966408
## 201 2 3 0.3305858741
## 202 2 3 0.2240620210
## 203 3 2 0.4192113564
## 204 3 2 0.5153542828
## 205 3 2 0.3269473275
## 206 3 2 0.4974781450
## 207 3 2 0.4658767010
## 208 3 2 0.4898643602
## 209 3 2 0.4862980661
## 210 3 2 0.4699210077
## 211 3 4 0.4479082560
## 212 3 4 0.1412552009
## 213 4 2 0.1114151238
## 214 2 4 0.3846130087
## 215 2 3 0.2453496539
## 216 3 2 0.4687798288
## 217 3 2 0.2164488661
## 218 2 3 0.2281040465
## 219 3 2 0.2579895945
## 220 3 2 0.5225980095
## 221 3 2 0.4787943949
## 222 3 2 0.5160164498
## 223 2 3 -0.0625169397
## 224 2 1 0.1260787832
## 225 2 3 0.2981279376
## 226 3 2 0.2767955344
## 227 2 3 0.0227994335
## 228 2 3 0.1914224246
## 229 3 2 0.5278855487
## 230 3 2 0.5357939273
## 231 3 2 0.2011659906
## 232 2 4 0.3585779975
## 233 3 2 0.2121423186
## 234 3 2 0.5099628372
## 235 3 2 0.1585141118
## 236 2 3 0.3402491167
## 237 2 3 0.3658297536
## 238 2 3 0.2490442975
## 239 3 2 0.1686692814
## 240 3 2 0.3917375807
## 241 3 2 0.3838895721
## 242 3 2 0.3729269768
## 243 3 2 0.5126910630
## 244 3 2 0.5252380448
## 245 3 2 0.1464977459
## 246 3 2 0.5064918533
## 247 3 4 0.4555713512
## 248 4 3 0.0466045617
## 249 4 2 0.1243470959
## 250 2 3 0.1108538702
## 251 3 2 0.4184337053
## 252 3 2 0.2725404125
## 253 2 1 0.2778655368
## 254 2 3 0.1415769757
## 255 3 2 0.4979358398
## 256 3 2 0.3914211501
## 257 2 3 0.2610206719
## 258 2 4 0.2186540200
## 259 2 3 0.2738564510
## 260 3 2 0.3716198919
## 261 3 2 0.1954243682
## 262 2 3 0.0423588001
## 263 2 3 0.1248126357
## 264 3 2 0.3405409012
## 265 3 2 0.4965295055
## 266 3 4 0.5239039907
## 267 3 4 0.4973743843
## 268 3 2 0.2137994876
## 269 2 3 0.2032125206
## 270 2 4 0.2076486325
## 271 2 1 0.1539570767
## 272 1 4 -0.0115176383
## 273 2 3 -0.0225477198
## 274 3 2 0.4140659324
## 275 3 2 0.4832570676
## 276 3 4 0.5031475187
## 277 3 2 0.3459277382
## 278 3 2 0.3513490426
## 279 3 2 0.2796938539
## 280 2 4 -0.0445630981
## 281 4 3 0.0852337814
## 282 3 4 0.0339220685
## 283 3 4 0.4572620610
## 284 3 2 0.5053612405
## 285 3 2 0.3475298548
## 286 3 2 0.2670776413
## 287 2 3 -0.0492416058
## 288 2 4 0.0503954028
## 289 2 4 0.2192171065
## 290 3 4 0.2675845276
## 291 3 2 0.4251333263
## 292 3 2 0.4847797146
## 293 3 2 0.5463981719
## 294 3 4 0.5091049241
## 295 3 2 0.4547368118
## 296 2 3 -0.0688241825
## 297 4 2 0.1137233437
## 298 4 2 0.2115136092
## 299 4 2 0.2627964367
## 300 4 2 0.1578221177
## 301 2 4 0.1926801492
## 302 2 4 0.1811557651
## 303 2 3 0.3114683602
## 304 3 2 0.2909466681
## 305 3 4 0.2844400776
## 306 2 4 -0.0801811943
## 307 2 1 0.1216265340
## 308 3 2 0.0939715756
## 309 2 3 -0.0620336643
## 310 3 2 0.2465072126
## 311 3 4 0.4041980246
## 312 3 4 0.3131909969
## 313 3 4 0.3997470379
## 314 3 4 0.4045983171
## 315 3 4 0.3375018716
## 316 3 4 0.1464339834
## 317 3 4 0.1340848704
## 318 3 4 0.1389705964
## 319 2 3 0.0497804214
## 320 2 1 0.2505747110
## 321 2 1 0.0531903262
## 322 4 2 0.4495500783
## 323 4 1 0.3492960673
## 324 2 4 0.2916836611
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## 2200 4 1 0.3301707538
## 2201 4 1 0.4125816313
## 2202 4 1 0.1258965432
## 2203 4 1 0.3576402606
## 2204 4 1 0.4761499764
## 2205 4 1 0.2098624376
## 2206 1 4 0.3423333299
## 2207 1 4 -0.1415244706
## 2208 4 2 0.4323998771
## 2209 4 3 0.3740367447
## 2210 4 3 0.3098632896
## 2211 4 1 0.1898573904
## 2212 4 1 0.2678504333
## 2213 4 3 0.4885925578
## 2214 4 1 0.4826346708
## 2215 1 4 0.1220608446
## 2216 1 4 -0.0632731702
## 2217 1 4 -0.0658347537
## 2218 2 1 0.1043585929
## 2219 1 2 0.0163431568
## 2220 1 4 0.2224613406
## 2221 1 2 0.1085729669
## 2222 1 4 0.1093414110
## 2223 2 1 0.1046820074
## 2224 4 3 0.3381855886
## 2225 4 3 0.2550150586
## 2226 4 2 0.3763321085
## 2227 4 2 0.2424553045
## 2228 4 3 0.3494919180
## 2229 4 3 0.2429482954
## 2230 4 2 0.2423585568
## 2231 4 2 0.1647701615
## 2232 4 3 0.3614788345
## 2233 2 3 0.1977634209
## 2234 4 3 0.1010305712
## 2235 2 4 -0.0303960142
## 2236 2 4 -0.0774102270
## 2237 2 4 0.2461130640
## 2238 4 2 0.1375276673
## 2239 1 2 0.0266749464
## 2240 4 1 0.3375503093
## 2241 4 3 0.2508093661
## 2242 3 2 0.3127938671
## 2243 2 3 -0.0693181283
## 2244 3 4 0.5187868081
## 2245 3 4 0.4327863561
## 2246 3 4 0.3714631380
## 2247 2 3 -0.0044011192
## 2248 2 1 0.2504712817
## 2249 2 1 0.0638847246
## 2250 2 4 0.2495208523
## 2251 2 4 0.1891500923
## 2252 2 4 0.1470620722
## 2253 2 4 -0.0580411825
## 2254 3 4 0.2795152808
## 2255 3 4 0.4480745079
## 2256 3 2 0.4590713825
## 2257 3 4 0.4817258429
## 2258 3 2 0.5345956046
## 2259 3 4 0.5066516813
## 2260 3 4 0.4382915414
## 2261 3 2 0.2743020564
## 2262 3 2 0.1179894422
## 2263 2 4 0.1774739792
## 2264 2 1 0.1194462894
## 2265 2 4 0.3126640334
## 2266 2 4 0.3352881776
## 2267 2 4 0.1772610226
## 2268 2 3 -0.0275646394
## 2269 3 2 0.2301467001
## 2270 2 4 0.1479540006
## 2271 2 3 0.2517153758
## 2272 3 2 0.3705807180
## 2273 3 2 0.4921025981
## 2274 3 2 0.3362116945
## 2275 3 4 0.3613471632
## 2276 3 2 0.3402095519
## 2277 3 2 0.5103865268
## 2278 2 3 0.2096379566
## 2279 2 1 0.2529239014
## 2280 2 4 0.1831046909
## 2281 2 3 0.3264757453
## 2282 2 3 0.3536655871
## 2283 3 2 0.3503004410
## 2284 3 2 0.4873025056
## 2285 3 2 0.3789216668
## 2286 3 2 0.4700581547
## 2287 3 4 0.5122766809
## 2288 3 2 0.4549885266
## 2289 3 2 0.3003511329
## 2290 3 2 0.5383088055
## 2291 3 2 0.5516206277
## 2292 2 3 0.1023778293
## 2293 3 2 0.3686906695
## 2294 2 4 0.2824393479
## 2295 2 4 0.1655664910
## 2296 2 4 0.2912438482
## 2297 2 3 0.2600002971
## 2298 2 4 0.0080791215
## 2299 2 3 0.0654694756
## 2300 2 3 0.1599058407
## attr(,"Ordered")
## [1] FALSE
## attr(,"call")
## silhouette.default(x = kmeans.result$cluster, dist = dist(data.cr))
## attr(,"class")
## [1] "silhouette"Cluster 2 a des silhouettes proches de 1, donc bien placés. Cluster 1 a des individus dont les silhouettes sont négatives, donc mal placés.
PAM
pam.result <- pam(data.cr, K)
pam.result## Medoids:
## ID MinTemp MaxTemp Rainfall Humidity9am Humidity3pm Pressure9am
## [1,] 1465 0.1682661 0.4643129 -0.3243074 -0.4104022 -0.4142087 0.2924229
## [2,] 1800 1.0711497 1.2798301 -0.3243074 0.4060714 0.5087682 -0.6204501
## [3,] 554 -0.5901561 -0.5365490 0.5004635 0.7326608 0.6765822 -0.9247412
## [4,] 625 -0.9151943 -0.8701697 -0.3046700 -0.9002864 -0.6659297 0.8473065
## Pressure3pm Temp9am Temp3pm AvgTemp
## [1,] 0.2142630 0.2695290 0.2564509 0.3245658
## [2,] -0.4872648 1.2873306 1.0781070 1.2122462
## [3,] -1.0041800 -0.5220945 -0.4905092 -0.5820013
## [4,] 1.0265583 -1.0121472 -0.7892933 -0.9219640
## Clustering vector:
## [1] 1 2 2 2 2 2 2 2 2 2 2 1 1 1 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2
## [38] 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1
## [75] 1 1 1 1 1 1 2 2 2 1 1 1 1 1 2 1 2 2 2 2 1 1 1 1 3 2 2 2 2 1 1 1 1 1 1 1 1
## [112] 1 1 1 2 1 1 1 1 1 1 4 1 1 1 3 3 3 3 3 3 3 3 3 3 3 1 3 3 1 1 3 3 3 3 3 3 4
## [149] 3 3 2 1 1 1 3 3 3 3 4 3 4 4 4 4 4 4 4 3 3 4 4 3 4 4 4 4 4 3 4 4 4 4 4 3 3
## [186] 4 4 3 4 4 4 4 4 4 4 3 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 1 1 3 3 4 4 3 4 4 4 4
## [223] 4 3 3 4 3 3 4 4 4 3 4 4 4 3 3 3 4 4 4 4 4 4 4 4 4 1 1 3 4 4 3 3 4 4 3 3 3
## [260] 4 4 3 3 4 4 4 4 4 3 3 3 2 4 4 4 4 4 4 4 1 1 1 4 4 4 4 3 3 3 4 4 4 4 4 4 1
## [297] 1 1 1 1 3 3 3 4 4 1 3 4 3 4 4 4 4 4 4 4 1 1 1 3 3 1 1 3 1 4 4 4 4 1 1 1 3
## [334] 1 1 3 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [371] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [408] 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 3 1 1 2 2 1 1 1 1 2 2 2 2 2 2 3
## [445] 2 2 2 2 2 2 2 1 3 2 1 3 3 3 3 1 1 3 3 1 1 3 1 4 4 4 4 4 4 4 1 3 3 3 3 4 4
## [482] 4 3 3 3 3 1 1 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 4 3 3 4 4 4 4 4 4 4 4 4 3 3 3
## [519] 3 3 4 4 3 3 4 4 4 4 4 4 4 3 3 3 3 3 3 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 3 3 3
## [556] 3 3 4 4 4 3 4 4 4 3 4 4 4 3 3 4 4 3 4 4 4 4 4 4 4 4 4 3 4 3 3 3 4 4 4 4 4
## [593] 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 4 4 4 3 3 3 3 4 4 4 1 3 4 4 4 4 4 4 4
## [630] 4 4 1 1 3 3 3 3 3 3 3 4 4 4 4 1 1 1 3 1 4 4 4 1 1 1 1 1 1 1 2 1 1 1 1 1 1
## [667] 2 2 2 2 2 3 1 1 2 3 2 2 2 2 2 1 1 1 1 1 1 2 1 1 2 3 3 2 2 2 2 2 3 1 1 2 2
## [704] 2 1 1 1 2 2 1 1 1 2 2 2 2 2 2 2 2 1 1 2 2 2 1 2 2 2 2 2 2 2 3 3 2 2 2 2 2
## [741] 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 2 2 2 1 1 2 2 1 2 2 2 2 1 1 2 2 2 2 2 3
## [778] 1 2 2 2 1 1 1 1 3 2 2 2 3 2 2 2 3 2 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2
## [815] 1 1 1 2 3 4 4 4 1 1 3 1 1 1 1 1 1 3 4 3 4 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4
## [852] 4 3 3 3 3 4 4 4 3 3 3 3 4 4 4 1 4 3 4 4 4 3 4 4 4 4 3 3 3 3 4 4 3 4 4 4 4
## [889] 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 4 4 3 3 4 3 4 3 4 3 4 4 4 4 4 3 3 3 4 4 4
## [926] 4 4 4 3 4 4 4 4 4 4 4 3 3 4 3 4 4 3 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4
## [963] 3 3 3 3 3 4 3 4 4 3 4 4 4 4 4 1 3 3 3 4 3 1 4 4 4 4 4 4 4 1 3 3 3 3 3 4 3
## [1000] 4 3 4 4 3 3 4 4 4 4 4 4 4 4 3 4 4 1 1 1 2 3 3 2 3 3 1 4 1 1 1 1 1 2 2 2 2
## [1037] 1 1 2 1 1 2 2 1 2 2 2 1 1 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1 2 2 1 1 2 1 1 1
## [1074] 2 2 2 2 2 2 2 2 1 1 1 1 2 1 1 1 1 1 2 2 2 1 2 2 2 1 1 1 1 1 1 3 1 1 3 3 2
## [1111] 1 1 2 2 2 1 1 1 2 1 1 1 1 1 1 1 3 1 3 1 4 4 4 1 4 4 3 3 3 3 3 3 3 3 3 3 3
## [1148] 3 3 3 4 4 4 4 4 4 1 3 3 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 4 4 4 4 4 3 3 4 4
## [1185] 4 4 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 3 3 3 3 4 4
## [1222] 4 4 3 3 3 3 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3
## [1259] 3 3 4 4 3 3 4 3 3 3 3 3 3 3 3 1 3 3 4 4 4 4 1 3 3 3 3 4 4 1 1 4 1 3 4 4 4
## [1296] 4 4 4 4 4 1 1 3 3 4 4 1 3 1 4 4 4 3 1 3 1 4 4 4 1 1 1 1 1 2 2 3 3 3 3 3 3
## [1333] 2 2 2 3 1 2 2 3 1 2 2 2 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1
## [1370] 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 2 2 3 2 2 2 2 2 2 1 1 1 1 1 2 2 2 3 3 2
## [1407] 2 1 1 1 2 1 1 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 1 1 1 1 1 1 1 1 1 1 2 3 2 2
## [1444] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 3 3 1 1 2 2 2 2 2 2 2 1 1 1
## [1481] 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 4 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 1 4 4
## [1518] 3 3 4 4 4 4 4 3 3 3 3 3 3 3 3 3 4 3 3 3 3 4 4 4 4 4 3 3 1 4 4 4 3 3 4 4 4
## [1555] 4 3 3 3 3 4 3 3 3 3 4 4 4 3 3 3 3 4 4 4 4 4 4 4 4 4 3 3 3 3 4 4 4 4 4 4 4
## [1592] 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 3 3 3 4 4 4 4
## [1629] 3 3 3 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 1 1 3 4 4 4 4 4 1 3 3 4 4 4 4 4
## [1666] 4 4 4 4 1 1 1 1 1 2 2 3 4 4 1 1 4 1 4 1 1 4 4 1 2 1 1 1 1 1 1 1 1 1 2 1 1
## [1703] 1 1 1 1 1 1 1 1 1 1 2 2 2 3 3 3 2 2 2 2 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [1740] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2
## [1777] 2 1 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 1 1 1 1
## [1814] 2 1 1 1 1 1 1 2 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 1 1 1 1 1 1 1 1 1 1 2 2 2 2
## [1851] 1 1 1 1 1 1 2 2 2 2 2 1 1 1 1 1 3 1 4 4 4 4 4 4 1 3 4 4 4 4 4 4 4 1 3 1 3
## [1888] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 1 3 4 4 4 4 4 4 4 4 4 4 4 4 3 3 4 4 3 3 4 4
## [1925] 4 4 4 3 3 4 3 3 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 3 3 4 4 4 4 4 4 4 4 4 4
## [1962] 4 4 4 4 4 4 4 4 4 4 4 4 4 1 3 1 4 3 3 4 4 4 4 4 4 4 4 4 4 4 1 1 3 4 4 4 3
## [1999] 3 3 4 4 4 4 4 4 4 4 4 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 2 4 4 4 4 3 4 4
## [2036] 4 4 3 4 4 1 1 1 3 1 4 1 2 2 3 4 1 1 1 2 1 2 1 2 2 2 2 2 2 1 1 1 1 1 2 1 1
## [2073] 1 1 2 2 2 3 1 1 1 1 1 1 1 1 1 1 1 2 2 2 3 3 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2
## [2110] 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2147] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2
## [2184] 2 2 2 1 1 2 1 1 2 2 2 2 2 2 2 2 1 1 2 1 1 2 2 2 1 1 1 1 1 1 1 2 2 2 3 3 2
## [2221] 2 2 3 1 1 1 1 1 1 1 1 1 3 1 1 1 3 1 3 1 1 4 4 4 4 4 1 3 3 3 3 3 1 4 4 4 4
## [2258] 4 4 4 4 1 3 3 3 3 3 3 4 3 3 4 4 4 4 4 4 3 3 3 3 3 4 4 4 4 4 4 4 4 4 3 4 3
## [2295] 3 3 3 1 3 3
## Objective function:
## build swap
## 1.944706 1.910137
##
## Available components:
## [1] "medoids" "id.med" "clustering" "objective" "isolation"
## [6] "clusinfo" "silinfo" "diss" "call" "data"par(mfrow=c(1,2))
plot(pam.result)
# le premier graphe correspond à l'ACP.
# le deuxième graphe aux silhouettes.
table(pam.result$clustering, kmeans.result$cluster)##
## 1 2 3 4
## 1 0 53 40 426
## 2 388 0 0 214
## 3 43 400 7 1
## 4 0 15 713 0res=FAMD(dataReady)## Warning: ggrepel: 2276 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps
## Warning: ggrepel: 2276 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps
On lance CAH avec la fonction HCPC
cah = HCPC(res, nb.clust = 4)
